The 20-year-old damaged the lateral collateral ligament in his left ankle during training last week and was subsequently ruled out of Canada's upcoming Gold Cup campaign.
Davies has returned to the Allianz Arena for treatment, but it is not yet known how long he will be out of action, although surgery is not required.
"Alphonso Davies faces a period on the sidelines at FC Bayern," a statement on the German club's official website read on Monday.
"The 20-year-old suffered an LCL tear to his left ankle in Canada's build-up to the Gold Cup. Davies has now returned to Munich for rehab.
"The injury will be managed without invasive treatment."
Davies also missed six weeks of last season with an ankle injury that restricted him to 35 appearances for Bayern in all competitions.
He led defenders in the German top flight last season for dribbles completed per 90 minutes (3.21) – among those to have played at least twice.
However, Bayern won nine, drew three and lost none of the 12 Bundesliga games they started without Davies in 2020-2021.
The German champions, now coached by Julian Nagelsmann, could also be without fellow left-sided defender Lucas Hernandez for the start of the new season.
Hernandez underwent surgery last week after tearing the medial meniscus of his left knee during France's 2-2 draw with Portugal at Euro 2020, ruling him out "for a few weeks".
Bayern, which saw David Alaba join Real Madrid on a free transfer in May, begins its title defence away to Borussia Monchengladbach on 14 August (AEST).