The Kings had sent Quick back to Los Angeles on Wednesday for further examination and an MRI test showed the injury.
Sutter said Quick can begin rehabilitating the injury immediately, but said there was no timetable for him to return.
"We’re obviously confident in him," Sutter told reporters. "We haven’t seen him play that much. His [first] start on the road this year was a shutout in Florida, and he’s been in [five] times and has played really well for us off the bench, so we’re looking forward to seeing him."
Quick was injured in overtime of the Kings' game Tuesday at the Buffalo Sabres when he stretched to make a save.