Griese played college football at the University of Michigan from 1993 to 1997. Michigan did not offer him a scholarship, so he walked on to the football team. He turned down scholarship offers from Purdue (his father's "alma mater") and Kentucky. After he was redshirted in 1993 and limited to placeholding duties in 1994, Griese took over as the starting quarterback after Scott Dreisbach was injured five games into the 1995 season. Griese started for the remainder of the 1995 season, capped by an upset of #2 ranked Ohio State, 31–23.