Boateng was injured midway through the 2-1 Bundesliga victory over Hamburg SV in the first game back after the winter break.
Bayern have said the adductor muscle injury would rule him out for "a longer period of time" with some estimates putting his absence to as long as three months.
"We have to remain calm. SOS solutions, like the ones doing the rounds at the moment, are not helpful," Rummenigge wrote in the matchday magazine for Sunday's league game against Hoffenheim."
"Good players are not being sold in the winter. Emergency transfers are exactly what they are and they also cost money."
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Boateng's injury has also alarmed Germany coach Joachim Loew, who promised to wait for a long as possible to include him the squad for this summer's Euro 2016 in France.
Bayern, eight points clear at the top of the Bundesliga and chasing a treble of titles, were already struggling with injuries before Boateng joined the list.
Franck Ribery, Juan Bernat and Mario Goetze are still working towards their comeback while defender Medhi Benatia is sidelined as well.
Rummenigge also backed coach Pep Guardiola, who will be leaving at the end of the season after three years in charge, saying any discussion about the coach now being a 'lame duck' was wrong.
"Pep Guardiola will get the full support from everyone who has a say at Bayern Munich until his very last working day here. You can tell that to those who want to start a lame duck discussion."
Guardiola turned down a contract extension late last year, saying he would like to move to a club in England's Premier League.
While he is on track for his third straight league title with Bayern -- and a record fourth consecutive for the club -- failure so far to win the Champions League with them has piled pressure on the Spaniard.
They face Italy's Juventus in the round of 16 of the competition next month.
"We are looking forward to the next four months with Pep, to exciting and hopefully successful football," Rummenigge said,
(Reporting by Karolos Grohmann, editing by Ed Osmond)
