Is there any word to designate prejudice against someone based on the degrees he holds or the university he attends/attended?
Credentialism seems to fit.
undue emphasis on credentials (as college degrees) as prerequisites to employment
This definition suggests that the word is most commonly used about employment discrimination specifically, and that agrees with my own intuition (although I don't think it's absolutely limited to this context – it might also be used when talking about the perceived credibility of authorities).
In the context of social discrimination or general negative attitudes towards people with less education, I think Hot Lick's suggestion of elitism might work better.