An MRI revealed the extent of the injury Friday.
Brogdon, the reigning NBA Rookie of the Year, had to be helped from the court after an uncontested layup attempt in the second quarter of Thursday's loss to the Minnesota Timberwolves.
Brogdon is averaging 13.3 points, 3.2 assists and 3.3 rebounds this season. Last year, he became the only non-first-round winner of the Rookie of the Year award, beating out the Philadelphia 76ers duo of Joel Embiid and Dario Saric.
"It's unfortunate that he got hurt," Bucks interim coach Joe Prunty said. "We understand that it's part of the game and we know that. He's tough minded and he'll battle through this. We'll move forward and we talked about it a lot -- the next guy be ready to play."
The injury comes at a time when Milwaukee (27-23) is set to get Jabari Parker back from a knee injury Friday against the New York Knicks. Parker was the second overall pick in the 2014 draft, but tore his left ACL for a second time last February and hasn't played since.
Information from ESPN's Nick Friedell was used in this report.