In a statement later Thursday, the team said Nance would be out two to four weeks. The team said he will undergo treatment and rehabilitation and his status would be updated accordingly.
Nance, 26, underwent an MRI on Thursday after leaving Cleveland's loss to Indiana on Tuesday. He did not play against New Orleans on Wednesday.
Nance, who signed a four-year, $45 million contract extension in October, is averaging 8.8 points and 7.5 rebounds for Cleveland this season.
The Cavaliers are 8-34 and have been beset with injuries, including to All-Star forward Kevin Love.