The former No. 1 overall pick went through a series of tests earlier this week that revealed the injury. Bogut will need exercise and rest, but no surgery is scheduled.
Bogut's injury is another blow to the Bucks, who are in eighth place in the Eastern Conference but have already lost leading scorer Michael Redd to a season-ending knee injury.
Bogut is averaging 11.7 points and a team-high 10.3 rebounds, but started suffering back spasms after a game Dec. 17 against Philadelphia.
Bogut had missed 13 of the last 18 games, and played under 17 minutes in his last two games before missing Tuesday night's loss at New Jersey.