Bogut suffered the injury Wednesday in a game against Houston and an MRI Thursday revealed the damage.
He has averaged 11.3 points and 8.3 rebounds in 12 games this season.
Bogut was the first player chosen in the 2005 draft and has spent his entire career with Milwaukee. He has a history of injuries, however, having played an entire 82-game in only his rookie season.
He played in 65 games last season and made 69 appearances the season before that. He has averaged 12.7 points a game in his career.