Davies, who recently returned to action after a long-term knee injury, was replaced by Hiroki Ito in the 50th minute after the Canadian collapsed and required medical treatment.
"Alphonso Davies suffered a torn muscle fibre in his right hamstring in the 3-2 victory over Eintracht Frankfurt. This was confirmed by ... FC Bayern’s medical unit," the side said in a statement.
"The defender will be sidelined for the time being."
While the length of Davies' absence remains unconfirmed, manager Vincent Kompany expressed hope he would return within two to four weeks.
"It doesn't look so bad," Kompany said after the match.
"I don't know if it will be two or four weeks," he told reporters. "My gut feeling is that it won't take that long."
Bayern, who are on top of the Bundesliga table with 60 points in 23 games, will face the second-placed Borussia Dortmund next Saturday.