The petition was begun after regent Pat Williams told The New York Times last week the university had "recruited thugs for its football team," the (Missoula, Mont.) Missoulian reported Wednesday.
Attorney Scott Gratton, who is circulating the petition, called on Gov. Steve Bullock and higher education officials to censure Williams and remove him from the Board of Regents.
The petition says labeling the players as thugs was "obviously untrue and knowingly damaging."
The comments by Williams, a former U.S. representative, alluded to crimes committed by UM football players in recent years. Former Montana running back Beau Donaldson was sentenced last month for rape.
The university system said last week that while it disagreed with Williams' comment, regents are entitled to their opinions.