"I'll be out for at least two weeks," Ilgauskas told the Cleveland Plain Dealer.
Ilgauskas missed Cleveland's 95-86 victory over Chicago on Sunday because of the injury. The Cavaliers said he will be re-evaluated after a week and no timetable has been established for when the 7-foot-3 center will return.
Ilgauskas didn't practice Saturday and was examined by team doctors.
Before Sunday's game, Cavaliers coach Mike Brown said, "More than anything else, it's a precautionary measure. He needs a rest."
Ilgauskas, one of the team's most consistent players, is averaging 13.5 points and 9.6 rebounds. He has 25 double-doubles this season and is second on the team in scoring behind LeBron James. Ilgauskas has started 58 of the Cavaliers' 60 games this season. He missed a game in Milwaukee on Feb. 26 with an upper respiratory infection.
Anderson Varejao started at center Sunday in place of Ilgauskas.
Guard Wally Szczerbiak, who missed Friday night's game, returned to the team and scored 17 points. His wife, Shannon, gave birth to the couple's third child Saturday.
The Associated Press contributed to this report.