Howard Wolowitz earned his master’s degree at the Massachusetts Institute of Technology, commonly called MIT.
Howard’s MIT background is central to his role as the group’s engineer. Unlike Leonard, Sheldon, and Raj, he does not hold a doctorate, but he has a master’s degree in engineering and works as an aerospace engineer at Caltech’s Department of Applied Physics.
The distinction becomes a recurring joke in the series. Sheldon often mocks Howard for being the only core male scientist without a PhD, while Howard points out that his engineering work has practical applications. His projects include equipment for NASA and the International Space Station, and he eventually becomes a payload specialist on the station.
The alternatives are other elite research universities, but they are not Howard’s alma mater in the show. Caltech is his employer, not the university where he earned his master’s degree; MIT is the specific canonical answer.