Bogut suffered a fractured tibia in his left leg just 58 seconds into his Cleveland debut during Monday's game against the Miami Heat.
Bogut had to be carried into the locker room by his new teammates with 11:38 left in the second quarter.
The team reported that initial x-rays and evaluation revealed the fracture in his lower leg. Bogut was taken to the Cleveland Clinic for further imaging and evaluation. The Cavaliers did not officially state that Bogut's season is over, but it is unlikely he will be able to return this season.
Bogut, 32, suffered the injury when he was called for a foul. He had no points, no rebounds and two fouls in his brief time on the court.
He was signed by the Cavaliers on Thursday for $385,000 as a free agent. He had been traded from the Dallas Mavericks to the Philadelphia 76ers on Feb. 23, then was waived by the 76ers four days later, making him a free agent.
This season Bogut averaged 3.0 points and 8.3 rebounds in 26 games, including 21 starts, for the Mavericks.
He started 66 games for the Golden State Warriors last season.