Gergiev, known for his warm ties with the Kremlin, had already faced pressure from other arts institutions wary of working with him since Russian forces invaded Ukraine on Thursday.
“I have made my position clear to Gergiev and also called on him to clearly and unequivocally distance himself from the brutal war of aggression that Putin is waging against Ukraine,” Munich mayor Dieter Reiter said in a statement.
“Should Gergiev not have clearly taken a stance by Monday, he can no longer remain chief conductor of our Philharmonic Orchestra,” Reiter said.
As well as being the principal conductor in Munich since 2015, Gergiev is also the chief of the Mariinsky Theatre in Saint Petersburg.
He has not yet spoken publicly regarding Moscow’s offensive, but he has proven fiercely loyal to the Russian president in the past, allying with him on the annexation of Crimea and a law aimed at stifling LGBT rights activists in Russia.
Gergiev has also faced pressure to speak out in Milan, where he is currently leading Tchaikovsky’s “The Queen of Spades” at the Teatro alla Scala.
If he doesn’t, “the collaboration will be over,” Italian media quoted Milan’s mayor as saying.
He was also suddenly dropped on Thursday from concerts where he was due to lead the Vienna Philharmonic at New York’s Carnegie Hall.
A spokesperson for the prestigious venue told AFP the decision had been taken “due to recent world events”.