Humber was drafted by the New York Yankees in the 29th round of the 2001 Major League Baseball draft. As the 875th pick overall, he described himself as "more of a draft-and-follow" prospect. The Yankees made Humber an offer in an attempt to lure him away from his college scholarship, but he did not sign, choosing instead to attend Rice University in order to play college baseball for the Rice Owls baseball team, competing in the Western Athletic Conference (WAC) of NCAA Division I.