No. It is not part of the Marvel Cinematic Universe
In an interview with Total Film, the director of the film said
"Very early on, when we were collaborating with Marvel, the decision was made to intentionally not connect it to the Marvel universe," director Don Hall told Total Film. "Everybody felt like it would be great for us to take this idea of theirs and make our own universe with it. Marvel really encouraged us to do that. So there'll be no Iron Man or Captain America, and no Avengers in this world. Our Avengers are the Big Hero 6."
John Lasseter has also said that the movie was made 100% independent of the comics.
“Not yet. No, we haven’t,” admitted Lasseter. “If we went directly into the Marvel Universe, that would mean we’d work more directly with Marvel,” and aside from some screenings that involved Joe Quesada, Marvel Entertainment’s chief creative officer, Big Hero 6 was a Disney project through and through. “Without question, it was made 100 percent here,” said Lasseter. “They’d forgotten the books existed.”