If you have the proteins purified, you may be able to detect their interaction by a change in intrinsic tryptophan fluorescence, assuming at least one of the proteins contains tryptophan residues. This would work best if at least one tryptophan residue is involved directly in the interaction.

Another approach would be to use fluorescence resonance energy transfer with extrinsic labels, a donor on one of the proteins and an acceptor on the other. The challenge is placing the labels in the right place. At least one of them could be on an antibody that recognizes an affinity tag.

One relevant point, as Adam mentions, is if you have purified proteins or if you are working with the proteins expressed in the cells you want to analyze them in. That will determine the manner of labeling. The second question is then how you detect the interactions. 

The first bit is straightforward: If you have purified proteins, use a protein labeling kit to attach a fluorophore to your protein and bring it into your cell via injection or load it via patch pipette. If you are dealing with expressed proteins things get a bit more complicated. Your best bet will be modifying them in some manner. Either by linking them to a fluorescent protein (which you want to avoid) or by using genetically targeted small molecule labels (e.g. SNAP-Tag, FlAsH, Halo-Tag). The latter tend to be smaller depending on which variant specifically you use, but they add an additional layer of experimental complexity. 

The second (and in my eyes much more fun :) part is detecting your effect. If you are trying to distinguish between cytoplasmic proteins (mobile!) and transmembrane proteins (or proteins interacting with these; much less mobile), fluorescence recovery after photobleaching ("FRAP") might be your best bet. After bleaching, mobile proteins will lead to a quicker recovery of the fluorescence than immobile ones. If you are imaging quickly enough, you can actually fit the fluorescence recovery time course and extract information on mobile vs. immobile fractions ...

If you are after "do my proteins interact or not", FRAP *might* help, but the differences will be minute. There, FRET might be useful, as Adam suggests. Alternatively, you could do something very wild: look at the polarization of the fluorescence light ("fluorescence anisotropy"). A bit tricky to set up and normally more suited to cuvette experiments. If you are interested in that, drop me a message. Depending on your sample, Michelle Digman's "RICS" (raster image correlation spectroscopy) might work. That has the advantage that you can do it using any regular confocal. 

Best of luck with your experiments!

You could also do microcalorimetry, which would give you a ton of thermodynamic information, but as Adam said, perhaps the most straightforward method would make use of the intrinsic tryprophan fluorescence. In addition to steady state emission and FRET, you could also use fluorescence anisotropy.

If the protein has just one accessible cysteine you can selectively conjugate any fluorophore for added specificity in your assay.

Thank you very much. I purify His-Tag proteins. Looks will use cyanide dyes and differential calorimetry since it doesn't require high amounts of purified protein. My mentor said that designing FRAP is very meticulous. Eventually we will use NMR, but we will need a lot of proteins for it..