The fracture was discovered in an MRI on Sunday in Salt Lake City.
Burks, 24, has had a strong season for the Jazz, averaging 14.3 points and 3.6 assists. He played only 27 games in 2014-15, with shoulder surgery ending his season.
Burks signed a four-year, $42 million extension that started this season.
Utah has been without center Rudy Gobert for three weeks with a knee injury, but his return is expected in the near future.