It is the second key player injury of late for Cleveland, which also is without point guard Kyrie Irving, who is recovering from a concussion.
Varejao was hurt in a Friday loss to Milwaukee as one of the Bucks tried knock the ball from him and nailed him on the wrist.
Initial X-rays Friday failed to reveal the fracture but it turned up during an examination Saturday at Cleveland Clinic.
Varejao is averaging 10.8 points and 11.5 rebounds this season.
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