Adrian Wojnarowski of ESPN reported the news, noting rookie Collin Sexton will start in the veteran's place.
Cleveland acquired Hill as part of its massive roster shakeup ahead of last season's trade deadline, and he helped the team reach the NBA Finals.
The 32-year-old Indianapolis native has dealt with some health woes in recent years. He was limited to 43 games during the 2014-15 season and 49 games in 2016-17 because of injury issues.
Sexton figures to see the majority of the playing time in Hill's place, especially since the 1-10 Cavaliers are in rebuilding mode and relying on his long-term development as a critical building block. They can also turn toward Rodney Hood as a versatile playmaker capable of handling the ball, and Jordan Clarkson provides backcourt depth.
Cleveland appears well on its way to a playoff-less campaign, but it could still use Hill's veteran leadership back in the lineup as it hopes to avoid falling too far behind in the Eastern Conference standings.