I once read that the divergence time between these two species is less than 12-24 MYA. At that point, I did not go to the original paper and now I can not find the reference.

@Tyler Chafin

Thanks for the reply.

I would like to know how diverged Mus musculus and Rattus novergicus are.

Which mouse and which rat? The terms "mouse" and "rat" are polyphyletic and do not correspond to phylogenetically informative groupings. There are multiple families which contain taxa called mice and rats- New World mice and rats, Old Worls mice and rats, Neotropical mice and rats, etc. Here is the current topology from the Tree of Life project: http://www.tolweb.org/Muroidea/16461

With that being said, I am going to assume you are talking about Mus and Rattus... Here is a recent paper on adding additional evidence to amend the previously held 12 my split:

Kimura et al. 2015 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4585935/

Looks like you posted your answer and my fixed response at the same time. Hope the linked paper helps.

@Tyler Chafin

Brilliant. Thanks so much. 

They are not as close as cow and buffalo

22.6 MYA is the average according to multiple studies. See http://www.timetree.org/ and type in Mus and Rattus

In reference to the 22.6 diveregence date one has to keep in mind that this is a minimal estimate. One can only say, in reference to this date, that rats and mice diverged at least 22.6 MYA

That's the average from timetree, not the minimum, I think. The range is 5-50 though so there's some error associated with it!