The Canadian, 21, has not played since 17 December after contracting Covid-19.
Bayern boss Julian Nagelsmann said a mild sign of myocarditis was discovered after Davies returned to training.
“During our follow-up examination that we do with every player that has had Covid-19, we detected signs of mild myocarditis,” said Nagelsmann.
“He has stopped training for now, so he won’t be available to us for the next weeks.”
Myocarditis is an inflammation of the heart muscle which can reduce the heart’s ability to pump blood and can cause rapid or irregular heart rhythms.
Davies has made 107 appearances for Bayern since signing from Vancouver Whitecaps in 2018, helping them win three Bundesliga titles and the Champions League in 2020.
“This myocarditis isn’t too dramatic based on the ultrasound, but more simply signs of an inflammation. Nevertheless, it needs to heal and that will no doubt take some time,” said Nagelsmann.
On 5 January Bayern said Davies was doing “well” after testing positive for Covid.
Nine Bayern players tested positive at the start of January after time away following the Bundesliga’s winter break.