Stanisic "tore the lateral ligament in his right knee" at training on Monday and will undergo an operation, Bayern said in a statement.
The 24-year-old returned to Bayern this summer after a season-long loan at Bayer Leverkusen, where he won the Bundesliga and German Cup double.
Bayern sporting director Max Eberl said on the club's in-house TV channel on Tuesday Stanisic, who has 20 caps for Croatia, "will be missing for the next few weeks, unfortunately."
Bayern, who finished trophyless last season for the first time in 11 years, are already light in defence.
New centre-back signing Hiroki Ito will miss the first few weeks of the season with a foot injury, while fellow central defender Matthijs de Ligt was sold to Manchester United earlier in August.
Bayern open the 2024-25 season on Sunday away at Wolfsburg.
