In theory, no. Much like the VEI (Volcanic Explosivity Index; from Newhall and Self, 1982, The Volcanic Explosivity Index: An estimate of explosive magnitude for historical volcanism, DOI:10.1029/JC087iC02p01231) which seeks to assign a scale of magnitude to volcanic eruptions, the moment magnitude scale is open-ended. Put simply, a bigger earthquake or eruption can always rate higher on their respective magnitude scales.

However, in practice, yes: there is an upper limit to earthquake magnitude. Because earthquake magnitude is a direct function of the energy released by the event, magnitude is also dependent on the LENGTH of the fault that ruptures (not to mention the tectonic setting; because of the mechanical properties of rocks, larger earthquakes are more likely in convergent settings). Longer instantaneous fault ruptures release more energy in one shock and thus generate a larger earthquake of greater magnitude. Based on this, the largest earthquake would be one that occurs on a fault whose length is equal to the maximum circumference of the Earth, and is subject to compressive stress. (Rocks are stronger in compression then tension, hence larger earthquakes occurring in subduction zones than spreading centers.) However, because such a geologic setting is infeasible at best and impossible at worst, the greatest possible magnitude is further constrained, to likely within the M10 range.

I'll see if I can't find a suitable technical paper to this end to pass your way (contributions from others also welcome), but in the meantime, because you mentioned it was a young student who initially posed the question, you might refer to this site (cf. attached link) put out by the Southern California Earthquake Center and the USGS exploring the scientific flaws of the movie "10.5". The language therein is easy for students of all levels and might aid comprehension.

http://www.earthquakecountry.info/10.5/MajorMovieMisconceptions/

The seismic moment depends on the average slip (displacement at rupture) and rupture area, as well as the driving shear stress (roughly stress drop) during the earthquake. The maximum rupture area relates to the strike dimension ('length') and dip dimension ('height' or 'width') of the rupture (slip) plane, and so does the slip. The maximum values of all these factors, and thus the moment, depend on the size of the seismogentic fault zone (or part of the zone) within which the earthquake occurs. For an earthquake to rupture the entire seismogenic fault zone, the local stress field in the entire  zone must be everywhere favourable to that type of fault slip, that is, stress-homogenised. There are certainly limits to how large a rock body - seismogentic fault zone or part of it - can develop stresses (that, in turn, relate to the strain energy stored in the body, a part of the elastic energy) that are everywhere similar and generally  favourable to a given type of slip at a particular time (the time of the earthquake). Thus the dimensions of the rock body/fault zone with favourable stresses for a particular earthquake at a particular time put limits on the maximum rupture area and slip and thus the moment (and the moment magnitude) of the earthquakes generated. Further discussion of these points is in: Gudmundsson A (2014) Elastic energy release in great earthquakes and eruptions.Front.EarthSci. 2:10. doi:10.3389/feart.2014.00010

Form theoretical point of view the answer is no, which means that there is no an upper bound.. The moment magnitude Iscale is an open-ended, one. The largest ever recorded was in the Chile earthquake of 1960 with moment magnitude equal to 9.6. The moment magnitude depends on the faults' dimension. But rocks can accumulate  finite maximum stresses and then release during the occurrence of a seismic event. Large faults can accumulate large amount of stresses (energy) so they release  large earthquakes of great magnitudes.

Besides all the above ideas the other colleagues have been well said, we must take into account that rocks have a finite resistance against stress, so this aspect limits the capacity of rocks to accumulate so much stress for a larger magnitude earthquake of about 10 and above degrees of magnitude.

So it is suppossed that earthquakes over about 10 degrees of magnitude are only possible by means of a meteoritic impact.

Tectonic stresses produce an increase in the elastic energy stored by the rocks up to one limit defined by its strength. When this strength is exceeded a rupture is produced and an earthquake is triggered. So, there is one upper bound to the energy that can be stored, and so to the seismic moment magnitude, defined by the rock strength. That was the view of Professor Ambraseys in his classes at Imperial College that I attended. He has written long ago some paper on this matter that you will be able to find. Another question is to define the value of this limit, as it will depend upon the rock mass involved and its heterogeneities, but never will increase infinitely, due to heterogeneities in the rock mass.

The practical upper limit is about 10, as David Jackson described at the Fall AGU a few years ago. Here's the link. This was perhaps the most entertaining talk on any subject I have ever attended.

http://abstractsearch.agu.org/meetings/2012/FM/sections/S/sessions/S24A/abstracts/S24A-08.html

As there is no saturation in estimation of seismic moment so there is no upper limit in estimation of seismic moment magnitude. This is as per physics and mathematics of earthquake sciences concerned. So far largest recorded/estimated earthquake in the world is May 22, 1960 Chile earthquake of magnitude 9.5.  

Well, a tectonic fault is certainly limited in space : length probably cannot exceed circumference of Earth (40 000 km), Width can't be significantly more than several hundreds of km (otherwise the rupture has to go into the deep viscous mantle) , and slip most probably cannot significantly excess 100m (if scaling laws are roughly correct).

seismic moment is Length x Width  x slip x mu

this gives us a max of several  10 exp(32), which means a maximum magnitude Mw of  around 11.

in conclusion : there's no room on Earth for an earthquake of magnitude 12 and more

Thanks Christophe,

it is a rough and simple estimation not yet published. Mw=11 could be enough for our Earth, I think.  

As a scale, it has no upper bound. It is open-ended as someone has already mentioned.

But physically speaking, it is constrained by scaling laws of rupture along fault planes, relating, length, seismogenic layer depth, stress drop and slip per event. Only I think the subduction slab may escape or bypass this scaling laws if the right concatenation of asperity breakages add to a much larger event, as it is being put in evidence by recent Mega-earthquakes on subduction zones.

Frictional/viscous rheology and last evidences about slow aseismic slip in megathrusts  are showing that is not possible to exceed too much the fault width (asperity dimensions). Moreover lateral heterogeneities (e.g. continental/oceanic crust transition) could easily stop an efficient seismic rupture. Thus fault length is limited too as discussed above by James Muller and others. The role of gravity and earth rotation in confining seismic ruptures is still an open question. To define an upper bound for moment magnitude with an uncertainty seems to be not so simple. I think no technical paper was focused on in the past and in any case Earth rheological models are rapidly changing. 

Physically: No

Practically: Yes, Due to the limited length of the fault and the maximum strain energy that can stored in the different types of rocks before reaching their failure points.

Length and width are not really a problem for a subduction slab!!!!! The physics behind is!!!!!! Concatenation of nearby asperities, one after rupture, triggering the neighboring one!!!!!

Both answers by Agust Gudmundsson and James Muller are correct. Theoretically, the moment magnitude scale has no limit, but the Earth and its plates and blocks are limited. Therefore, in fact, the moment magnitude scale has its limit. I can estimate, what value be this limit:

According to my research, the limit of energy accumulation depends on the thickness of the layer according to the relationship log(E)[J]=4.29*log(h)[m]-0.56 (Kalenda 1992 - PhD thesis). If we assume the rupture "width" of 30 km and the "length" of 100 - 300 km (normal ratio for typical faults), then the log energy [J] is 18.6. Then, the Richter magnitude will be approximately 9.3 according to the relationship log E = 5.24 + 1.44M. We can assume, that for "whole crust seismic events" the width of rupture will be constant app. 30 km, but the length will increase to the limit of the one side of the lithosphere plate (approx. 10000 km). Then, the seismic moment will increase 30 times and the moment magnitude will increase by 1 according to the relationship Mw=2/3 log(Mo)-6.

According to my estimation, the upper limit of moment magnitude for Earth is Mw=10.3. There is no possibility to accumulate such energy/moment to have Mw=12.

Attached paper of Dr. McCaffrey might be helpful to answer this question

There is a related article in nature, which gives a maximum Mw of about 9.7 from the reported M0 of 4.9E30 dynes cm; Upper limit to earthquake size. Nature 262, 378–379 (1976). https://doi.org/10.1038/262378a0