Burke, acquired from Minnesota after the Timberwolves selected him ninth overall in the NBA draft, returned to play nearly eight minutes in the second quarter before X-rays at halftime revealed the fracture.
Team doctors will further evaluate Burke's condition on Monday.
"We'll see what the specialists say, but it's definitely a downer for us," Utah coach Tyrone Corbin said. "This is another obstacle we'll have to overcome, but we'll put our heads together, see what we have and go from there."
Information from The Associated Press was used in this report.