The OED gives the 1965 citation from The American Economic Review:
A person who has a mentor; the person guided or tutored by a mentor.
1965 Amer. Econ. Rev. 55 862 What is the typical economics class but a contact between the conservative teacher and his mentees?
The terms protégé or apprentice are probably more common, but mentee gets the idea across well enough to me that I wouldn't consider it incorrect, especially considering that the OED and MW dictionaries have entries for it.
EDIT: Mentee is also not marked as rare or obsolete in these references, which is another (not perfect, but good) indicator that it is a usable word. In fact, the most recent citation is from 2001:
2001 Fast Company (Electronic ed.) 1 Jan. 58 Although Garrison doesn't think that mentors need to be best friends with their mentees, he does think that both partners should feel simpatico on some level.
…which is quite recent by OED standards. Furthermore, even if it did not appear in a dictionary, it could be usable as a nonce term. This happens often when the morphology or composition of a word makes its meaning clear. Mentee definitely qualifies, since it looks like the complement of mentor in an -or[er]/-ee suffixed pair. Nonce terms frequently enter the language (see affluenza and securitization), even if they are back-formed (see resurrection and burgle), like mentee is.
I'll include an nGram here of mentee against protege (accents removed to better fit with Google's OCR/ReCAPTCA results), since it seems to reflect a recent upsurge in the usage of mentee (though the usual caveats about nGrams should be taken into account). Even though the latest data points reflect a ~7:1 preference of protege to mentee, the latter still enjoys 53,000 printed book search results, most of which are from the last 3 years of the data sample (1997-2000).
