The 22-year-old tore ligaments in his right ankle after an hour of Bayern's 2-0 win over Nurnberg at the weekend and will now need to rest for five to six weeks before beginning light training, the Bavarian club announced on their website.
"We're going to miss him," said Bayern coach Pep Guardiola at a press conference.
"He's a very special player and important to the team, but he's going to be out for a long time."
The Spaniard will be on crutches for the next six weeks, meaning a return is unlikely until November at the very earliest.
He will miss at least Bayern's next four Bundesliga fixtures while he could be ruled out for three Champions League encounters.
He will also not feature in the UEFA Super Cup against Chelsea on Friday.