Schweinsteiger, who has been nursing a patella tendon injury in his left knee for months and needed treatment during Germany's victorious World Cup campaign in June and July, has not yet played this season.
"Our doctor is confident this will not be a long-term issue," Rummenigge told reporters at a club event in Munich.
"But obviously this is not an issue of one or two weeks. It may last a little more than that and we just have to be a bit patient."
Schweinsteiger looks like missing Germany's friendly against Argentina on Sept. 3 as well as the Euro 2016 qualifier against Scotland a few days later.
He is not the only injury concern at Bayern with fellow midfielder Javi Martinez sidelined for the rest of the year with torn cruciate ligaments.
Defender Rafinha and midfielder Thiago Alcantara are also long-term injury victims while Franck Ribery missed last week's German Super Cup final defeat by Borussia Dortmund and the 4-1 German Cup first-round win over Preussen Muenster.
Coach Pep Guardiola, who earlier this month ruled out any more incoming transfers, said last week the team needed a replacement for Martinez.
The Bundesliga starts on Friday with Bayern taking on VfL Wolfsburg.
"Whether or not we will be active in the transfer market depends on the quality on offer and the price," said Rummenigge.