Davies is due to undergo surgery on Wednesday and will be out for at least six months. Upamecano will not be available to the club for "several weeks", the Munich club said.
This means the duo will be out of the Champions League clash with Inter Milan for the time being.
"Unfortunately, during international breaks there's always the risk that players will return injured - this time it’s hit us particularly hard," Bayern's director of sport Max Eberl said in a statement.
"The absences of Alphonso Davies and Dayot Upamecano are a heavy blow for Bayern. Phonzy will get all the support he needs on his way back. We will also follow Upa closely in the coming weeks and assume that he will be available again soon. Our squad is strong and will compensate for these absences," Eberl added.
Canadian had to leave the pitch early
Davies went down early in the match for third place in the CONCACAF Nations League against the USA, holding his right knee. He was substituted in the 12th minute and returned to the sidelines after brief treatment with an ice pack on his knee.
Munich CEO Jan-Christian Dreesen had given the all-clear after receiving positive feedback from Canada. Back in Munich, Davies was thoroughly examined and a diagnosis was made.
Upamecano was last in action with France. Last Sunday, he converted the decisive penalty in the Nations League quarter-final second leg to win 5-4 against Croatia.