Yes why not?
See the Mechaber in YD 286.
Perhaps you are thinking that it should be the same as closets, which the velt is not ???? to put mezuzos on. However, the reason for that is probably because closets are less than 16 square ???? – approximately 24 – 32 square feet, or perhaps because you don’t go in and out of the closet. If they don’t meet this criteria then chances are they also require a mezuzah.
Oomis – ask your rav, I don’t see why not.