Burke, the ninth overall pick in this year's NBA draft who was acquired in a trade with Minnesota, will wear a cast or splint for the next three weeks before being re-evaluated. A source close to Burke told ESPN The Magazine's Chris Broussard that Burke's timetable to return is close to six weeks.
Widely expected to start for the Jazz, Burke averaged 18.6 points, 6.7 assists, 3.2 rebounds and 1.6 steals for Michigan last season, helping the Wolverines to the NCAA title game.
Burke broke his finger during last Saturday night's preseason game against the Los Angeles Clippers.
Information from The Associated Press was used in this report.