The Bavarians CEO cannot comprehend how the midfielder is not garnering complete respect on the back of a treble-winning campaign
The Germany international, a veteran of die Roten, was a crucial cog as Jupp Heynckes guided the club to Bundesliga, European and DFB-Pokal glory last season.
However, he has not been a regular under coach Pep Guardiola but Rummenigge dismissed outright any notion that Schweinsteiger is no longer a core member of the first team and slammed questions being raised about whether he will stay at the club.
"I am annoyed the constant criticism, the constant bickering, toward Bastian Schweinsteiger," the Allianz Arena chief wrote in the club's pre-Wolfsburg clash magazine. "He does not even begin to deserve it.
"We're talking about a man who, at just 29 years of age, has almost 100 caps for Germany, this year was at the forefront of our treble success and was nominated a few weeks ago for Germany's footballer of the year.
"He is an outstanding player who puts in one of the highest contributions to Bayern and has earned great respect worldwide. He will continue to be of enormous importance to us in the next few years.
"To deny him this respect and to ask him questions repeatedly does not suggest to me the best of intentions. I can not understand this discussion."
Bayern, who sit second behind Borussia Dortmund in the Bundesliga but on equal points, next face Wolfsburg on Saturday having overcome Hannover in the DFB-Pokal second round on Wednesday.