Burke will have the operation on Tuesday morning in Salt Lake City. Pins will be inserted to stabilize the point guard's right index finger, which he fractured during a 106-74 preseason loss to the Los Angeles Clippers on Saturday night.
The Jazz did not announce a timetable for Burke's return. Early reports said he was expected to miss anywhere from eight to 12 weeks, but a source close to Burke told ESPN The Magazine's Chris Broussard the timetable was closer to six weeks.
"It's unfortunate that it would happen now in training camp," coach Tyrone Corbin said after Monday's practice. "He was learning a new game and the way to play it and he was making great strides. And now he won't have a chance to be in a game for a little while. But he can learn in different ways."
Burke was penciled in as a starter after the Jazz acquired his rights from the Minnesota Timberwolves in a draft night trade.
Burke spent two seasons at Michigan, leading the Wolverines to the national championship game as a sophomore. He averaged 18.6 points, 6.7 assists, 3.2 rebounds and 1.6 steals while shooting 46.3 percent from the field and 38.4 percent from 3-point range in his final collegiate season before turning pro.
Corbin said the Jazz will work closely with Burke to keep him from falling behind during his absence.
"We'll have him watching," Corbin said. "We're going to miss him on the floor, but we're going to do some different things with him to keep getting him up to speed."
Veteran point guard John Lucas III likely will be the starter until Burke recovers. Lucas signed with the Jazz as a free agent during the offseason.
Lucas has appeared in 174 games during five NBA seasons, making a pair of starts with the Chicago Bulls in the 2011-12 season. He has career averages of 5.1 points and 1.5 assists.
Lucas doesn't feel extra pressure with his role suddenly changed from backup mentor to starter.
"I'm going to come in and do exactly what I've been doing," Lucas said. "Getting everybody involved. Keep knocking down shots. Keep trying to get wins."
Alec Burks, who ran the offense in limited minutes a season ago, could potentially slide over to the point to help out while Burke is sidelined. Beyond using Burks as an emergency point guard, the Jazz will look into trade options and signing potential free agents to shore up their backcourt depth.
Information from ESPN The Magazine's Chris Broussard and The Associated Press contributed to this report.