Kanter's injury came just hours after the Jazz announced starting point guard Mo Williams will be sidelined for at least six weeks and maybe much longer because of a thumb injury.
Williams is scheduled to undergo surgery on Friday.
The loss of Kanter will limit coach Tyrone Corbin's rotation in the frontcourt, where Al Jefferson, Paul Millsap and Derrick Favors will likely form a three-player rotation.
Kanter averages 6.7 points and 4.3 rebounds this season, but he's averaged 9.3 points over the last four games.
"It's another one of our guys down," Corbin said. "We'll miss him. Hopefully it's not very serious and he'll be back soon."
The Jazz play five of their next six games on the road, starting in Phoenix. They play a back-to-back at Denver on Saturday night.