Davies was taken off just after the hour mark in Bayern's 3-2 win at Hertha Berlin on Saturday. He will miss the defending champions' matches against Werder Bremen and Schalke before the World Cup break.
"The 22-year-old full-back tore a muscle fiber in his right rear thigh during the 3-2 away win at Hertha BSC on Saturday," Bayern said in a statement.
"Participation in the World Cup in Qatar is not in danger for the Canadian international."
Davies is one of Canada's key players at the World Cup, where the country will be making its first appearance since 1986, playing in Group F where they face Belgium on November 23 followed by Croatia and Morocco.