Joe Chialo, from the conservative CDU party, had initially sought to defend the cost-saving measures last year but became a lightning rod for anger during protests over the cuts.
However, he said Friday that extra measures now being planned went too far and could "lead to the imminent closure of nationally known cultural institutions".
Chialo also said discussions about the cuts had become difficult as criticism was increasingly focused on him personally.
"When central political and professional goals can no longer be implemented... it is, in my view, consistent to step aside and place the office in new hands," he said in a statement.
The 54-year-old had been seen as a contender for culture minister at the national level in the incoming CDU-led government of Friedrich Merz.
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But on Monday the party announced that Wolfram Weimer, a prominent conservative publisher and journalist, would take up the post.
Chialo was booed when he addressed a rally of hundreds of creative sector workers at Berlin's Brandenburg Gate in November, with techno clubs, classic music venues and theatres all warning the cuts would be devastating.
He was also in the headlines again in February when a report claimed that outgoing Chancellor Olaf Scholz had referred to him as a "fig leaf" figure in the CDU and a "court jester".
Scholz fiercely denied any suggestion that the comments were linked to the ethnic background of Chialo, who has Tanzanian family roots.
Some of Chialo's public events have also been disrupted by pro-Palestinian activists after he repeatedly condemned rising anti-Semitism in Germany amid the Gaza war that was sparked by Hamas's deadly October 7th, 2023 attack on Israel.
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