Coman had an operation on Monday (AEST) after sustaining a syndesmosis ligament tear in his left ankle.
The France international was hurt late in the opening half of Bayern's 3-1 home win over Hoffenheim on Friday and had to be helped from the field.
Bayern initially estimated Coman would miss "several weeks" of action but the Bundesliga champions gave no further timescale in a statement, noting the 22-year-old "faces a long spell on the sidelines".
Sporting director Hasan Salihamidzic said: "I'm convinced Kingsley will come back stronger. We'll support him all the way."
Bayern team-mates including Robert Lewandowski have shown support for Coman in his latest injury setback.
"You'll be back stronger," Lewandowski wrote on Twitter. "We are waiting for you Kingsley."