The teenager twisted his right ankle with barely a minute gone at the Allianz Arena.
Davies was in clear distress as he was helped off and replaced at left-back by Lucas Hernandez as Robert Lewandowski netted a hat-trick in the rout.
"He has injured ligaments - one is torn, one is partially torn. We expect him to be out for six to eight weeks," said Bayern head coach Hansi Flick.
"If a player of this quality drops out, it hurts."
Davies broke into the Bayern first-team last season and made the left-back berth his own - keeping out Bayern's record-signing Hernandez - as they won the treble of Champions League, Bundesliga and German Cup titles.
However, Hernandez started ahead of Davies at left-back in last weekend's 4-1 romp at Bielefeld and Wednesday's 4-0 rout of Atletico Madrid in the Champions League.
Last Tuesday, Flick said Davies had suffered a "dip" in form, but "with his speed and dynamic, he is an important factor" with Bayern facing a run of away games.
Bayern have Champions League trips to Lokomotiv Moscow and Salzburg in the coming fortnight before playing Borussia Dortmund away in the Bundesliga on November 7.