A team source told ESPN that Rose's numerous injuries are "taking a toll on him mentally".
Rose broke into the league as the No. 1 overall pick in the 2008 National Basketball Association draft out of Memphis and was part of the Chicago Bulls organization for eight years.
A team source tells ESPN: "He's exhausted of being hurt and it's taking a toll on him mentally". A team spokesman said Friday that Rose has been excused since Wednesday and there is no timetable for his return. He first suffered the injury on October 20 in Milwaukee, when he landed awkwardly after a flagrant foul by Bucks center Greg Monroe.
Because of this injury, he missed an entire 2012-13 season. He returned to play in five games but suffered a setback on November 7 and hasn't played since. He would later win the MVP with the team in 2010-11 season.
Rose was averaging 14.3 points per game for the Cavaliers.
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The team did not offer any other details about Rose's absence.
A three-time All-Star, Rose signed a one-year $2.1 million deal with the Cavs this offseason after spending last season with the Knicks.
He appeared in 51 games in 2014-15, 66 in 2015-16, his previous year with the Bulls after they drafted him No.1 in 2008. As a teammate put it, Rose has grown increasingly wary of the emotional pitfalls associated with recovering from injury - which is certainly something that the veteran signal caller has unfortunately become accustomed to over the years.
"Just a jacked-up ankle", Rose told ESPN before putting on the walking boot.