Heinlein never explicitly gives us any numbers, but it is implied to be very small. The books explicit state that, with the advent of smart rockets, nukes and other ways of dealing massive death from a distance, the MI is really only useful when the task involves something other than straight up death dealing.
In the books, Heinlein was always very specific in his military talk. He mentions the different divisions of the military on many occasions, and we hear about divisions up to the Fifth. The Fourth is never mentioned, but presumably it exists.
So we can be almost certain in an estimate of 4-6 divisions.