The injury was diagnosed after an MRI by team physician Steve Lombardo and Dr. Neal S. ElAttrache of the Kerlan-Jobe Orthopaedic Clinic in Los Angeles.
Blake was hurt in the second half of a 116-111 loss to the Washington Wizards on November 26.
New York Knicks point guard Raymond Felton will be out two to three weeks with a strained left hamstring.
Multiple media outlets reported the Knicks are now talking with the Toronto Raptors about getting Kyle Lowry, who became available when the Raptors picked up Greivis Vasquez in the Rudy Gay trade. For now, Pablo Prigioni is expected to start in place of Felton.
LeBron James of the Miami Heat and Paul George of the Indiana Pacers top the Eastern Conference, and Kevin Durant of the Oklahoma City Thunder and Kobe Bryant of the Los Angeles Lakers lead the Western Conference after the first returns of the NBA All-Star balloting.
James, the reigning NBA MVP and finals MVP, is the overall leader with 609,336 votes and Durant is second with 607,407 votes.
James, George (489,335) and the New York Knicks' Carmelo Anthony (424,211) pace the Eastern Conference's frontcourt players.
The Cleveland Cavaliers have recalled guard/forward Carrick Felix, guard/forward Sergey Karasev and center Henry Sims from the Canton Charge.
All three appeared in Wednesday night's 94-91 overtime win over Tulsa in Canton. Felix finished with five points, five rebounds and three assists in 19 minutes, Karasev added 16 points and three rebounds in 30 minutes and Sims had 12 points and nine rebounds in 24 minutes.