The 33-year-old full back, who captained Germany to the 2014 World Cup title, said on Tuesday he would retire one year before his contract ends at the end of next season.
He made the announcement after Bayern's German Cup last 16 win over VfL Wolfsburg and also said he had informed the club he would not take over the sports director role as widely expected.
Only minutes earlier Bayern president Uli Hoeness had told reporters he knew nothing of Lahm's retirement and said any announcement would be a joint one with the club.
"Bayern Munich are surprised by the actions of Philipp Lahm and his advisor," Rummenigge said in a statement.
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"Until yesterday we were expecting to issue a joint statement from Philipp Lahm and Bayern Munich.
"Uli Hoeness and myself had honest, intensive talks in the past months with Philipp about a potential involvement in the management of our club.
"Last week he informed us he was currently not available for the sports director position and that he wants to end his contract early."
Lahm is among Germany's most successful players of all time, having won almost every trophy with club and country, including seven Bundesliga titles, six German Cups, the Champions League, the Club World Cup and the World Cup.
He has spent almost his entire senior career at Bayern after coming through their youth system.
The diminutive defender was one of the world's best full backs for the better part of a decade, moving into a midfield role more often in recent seasons.
Lahm, who retired from international football after Germany's World Cup triumph in Brazil, had been seen as the perfect successor to Matthias Sammer as Bayern sports director but said the time was not right for such a move.
"We want to make it clear that the doors at Bayern Munich will remain open for Philipp," Rummenigge added.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
