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Burks, who is wearing a boot on the injured left ankle, suffered the injury on a foul by the Los Angeles Clippers' Paul Pierce on Saturday night.
The fracture was discovered in an MRI on Sunday in Salt Lake City.
Rodney Hood and Joe Ingles will have increased roles in Burks' absence.
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.