While Bogut will not require surgery, he is projected to be out from six to eight weeks.
An MRI on Tuesday revealed Bogut suffered bone bruises to his proximal tibia and distal femur, two major bones in the leg. The injury happened in a collision with Cleveland Cavaliers shooting guard J.R. Smith in Monday's Game 5.
Bogut contested a shot in the lane by Smith, who ran into Bogut's fully extended knee. He walked very gingerly as he left the arena Monday night.
Bogut traveled to Cleveland for Game 6 on Thursday, when the Warriors will try again to close out the Cavaliers and win their second NBA title in a row.
He said Thursday it is "very unlikely" he will recover in time to allow him to play for Australia in the Rio Olympics.
Bogut had five blocks in the Warriors' Game 2 victory, but his role had been limited during the series. He only averaged 12 minutes per game, putting up 3.2 points and grabbing 3 rebounds per game. He averaged 4.6 points and 5.7 rebounds in 22 postseason games.
"I've been in this position before; be aggressive," Ezeli told The Undefeated's Marc Spears. "Especially on the boards and in the paint. We win that way."
Bogut will be in the final year of his contract next season and is scheduled to earn $11 million.