The Bruins (25-9), who finished second in the Pac-12 Conference tournament, are the sixth-seeded team in the South Regional.
If UCLA beats the Gophers (20-12), it would play the winner of third-seeded Florida and No. 14 Northwestern State in the third round. The Sweet 16 in the South Regional will be held in Arlington, Texas.
The Bruins have a 5-1 record against Minnesota. The Gophers have four players averaging double figures, led by guard Andre Hill at 13.9 points. But Minnesota has a 5-11 record in its last 16 games.
Also in UCLA's portion of the South Regional bracket vying for spots in the Sweet 16 are second-seeded Georgetown, which plays No. 15 Florida Gulf Coast, and seventh-seeded San Diego State, which opens with No. 10 Oklahoma.