Kelsey Russo of The Athletic reported the news, noting Darius Garland (groin strain), Kevin Porter Jr. (concussion) and Dante Exum (ankle sprain) will also be sidelined.
Thompson missed time earlier this season with a quad injury and played just 43 games in 2018-19 and 53 games in 2017-18. However, he was durable in the early portion of his career and played at least 78 games five straight seasons from 2012-13 through 2016-17.
When healthy, he is a double-double threat every time he is on the floor who is averaging 12.0 points and 10.1 rebounds this season.
The University of Texas product averaged a double-double last season with 10.9 points and 10.2 rebounds per game and was a key part of the 2015-16 Cavaliers squad that won the championship behind LeBron James, Kyrie Irving and Kevin Love.
Cleveland will have to look elsewhere until the veteran is ready to return and will likely give more playing time to the combination of Andre Drummond, Love and Larry Nance Jr. while he is sidelined.