The Timberwolves announced Saturday that Rose had "successful arthroscopic surgery to remove bone chips from his right elbow."
Rose has not appeared in a game since March 10 because of the injury.
Minnesota has just 10 games remaining on its regular-season schedule, and it is 9.5 games out of a playoff spot, which all but ensures that it won't be returning to the postseason for the second year in a row.
While the Timberwolves have taken a step back as a team after reaching the playoffs for the first time in 13 years last season, Rose has enjoyed a resurgent campaign individually.
The 30-year-old veteran is averaging 18.0 points, 4.3 assists and 2.7 rebounds over 51 games after putting up just 8.4 points per contest in 25 games split between the Cleveland Cavaliers and Timberwolves last season.
Rose is a three-time All-Star and one-time NBA MVP who was once among the league's elite players with the Chicago Bulls. Multiple knee injuries beginning in 2011-12 derailed his career, however, and led to him getting traded to the New York Knicks in 2016.
Although Rose has been a productive player when healthy, he has missed 16 or more games in each of the past eight seasons.
With both Rose and Jeff Teague on the shelf, Tyus Jones will get the bulk of the minutes at point guard for Minnesota down the stretch. Also, Josh Okogie will carry the load at shooting guard.
Rose can become a free agent at the conclusion of the season, meaning it is possible he has played his final game as a member of the T-Wolves.