Coman was helped off the pitch early in the second half on Saturday, needing the assistance of two Bayern staff members as he could not put weight on his leg.
Bayern coach Thomas Tuchel said Coman would definitely miss Wednesday's second leg at home to Arsenal, while the forward's participation at Euro 2024 is also at risk.
The first leg of Bayern's European tie in London ended 2-2 on Tuesday.
"It's a big downer which overshadows the victory a little," Tuchel said at the post-match press conference.
Bayern sporting director Christoph Freund said Coman "still needs to do some tests but it doesn't look good."
"We hope it won't be counted in months. We'll see what the test says but we'll expect him not to be available for several weeks."
Tuchel said his side needed to "throw everything into it" against Arsenal on Wednesday, telling reporters "let's hope the home advantage is the decisive advantage."
Coman had only recently returned from a torn knee ligament that kept him out from January to March.
Euro 2024, to be hosted in Germany, starts on June 14th.
