The World Cup-winning midfielder had picked up a minor ankle problem in pre-season, but was reported to have been re-examined on Monday due to irritation around the patellar tendon.
And club chief executive Karl-Heinz Rummenigge confirmed on Tuesday that Schweinsteiger's recovery would take more than a couple of weeks.
"This is not a story of a week or two, but one that will take a bit longer," he said.
"We are optimistic there will be no long-term issue. We have to stop now and be patient for a few weeks."
The injury will keep Schweinsteiger out of the opening stages of Bayern's Bundesliga defence, which begins at home to Wolfsburg on Friday.
There will now also be doubts over whether the 30-year-old will be able to feature in Germany's first Euro 2016 qualifier against Scotland on September 7.
Bayern already have to come to terms with another injury to Javi Martinez, who requires knee surgery and will be out for several months.
Thiago Alcantara is another Bayern midfielder missing with a knee injury, though Rummenigge was quick to insist the former Barcelona man will not be rushed into action to replace Schweinsteiger or Martinez.
