"This has been a very challenging and difficult time for Derrick. We will continue to provide him with support and have patience as he re-joins his teammates and works his way back on to the court," Cavs general manager Koby Altman said in a statement.
Adrian Wojnarowski of ESPN first reported the news.
Rose, 29, left the team last month amid frustration over the mounting injuries that have derailed his career—most recently an ankle issue that has kept him off the court for most of the season.
LeBron James said Friday he has not spoken to Rose since before he left the team.
"Whenever he's ready to tell us or whatever, we're ready for that," James told reporters. "You don't ever fast-track someone's process of what they may be going through. When they're ready to talk about it or ready to bring it to the forefront, as his teammates, we'll be ready for it.
"I don't know what the organization's stand on that is. That's different. From us as players, we don't need an answer from him. We want him to be as great as he can be, off the floor first before he even thinks about being on the floor."
Rose, the 2011 NBA MVP, has had a once-promising career fall apart mostly due to injury issues. He suffered a torn ACL during the first round of the 2011 playoffs and played a total of 10 games over the following two seasons amid multiple setbacks.
Rose has played in at least 51 games each of the previous three seasons but has dealt with more injuries and has been a shadow of his MVP-level self. In seven games with the Cavaliers, Rose was averaging a career-low 14.3 points and 1.7 assists per game. Cleveland was consistently better with him off the floor and has reeled off an 11-game winning streak in his absence.
James has largely handled primary ball-handling duties with Rose and Isaiah Thomas out, and Dwyane Wade has done so as part of an improving second unit.
No timetable has been set for Rose's return to the floor.