Schweinsteiger has been plagued by injury problems this year and will consequently miss the start of the 2014-15 campaign, but Rummenigge is not overly concerned about the Germany international's fitness.
"Schweinsteiger has a problem with his kneecap and was examined again on Monday," Rummenigge said at a press conference.
"It's going to take a few weeks to clear up and he won't be fit for the internationals in early September.
"We'll have to be patient but we're confident it's nothing long-term."
Bayern are believed to be in the market for a new centre-back following Javi Martinez's serious knee injury, but Rummenigge has made it clear they will only sign someone if the conditions are right.
"It's not our intention to panic or get nervous. We're in good shape, as everyone saw in the DFB Pokal game [against Preussen Munster]," he added.
"We have lots of quality in the squad and we're very relaxed. If we do choose to do anything it'll depend on quality and price. We'll monitor the situation calmly."