Professor Peter Schäfer proposed his resignation “to avoid further damage” to the Jewish Museum, a statement on its website said. It was accepted, the statement added, but no specific reason for his departure was given.
The German parliament last month condemned the BDS movement — which stands for Boycott, Divestment, Sanctions — as anti-Semitic.
Lawmakers said the group uses anti-Semitic methods to promote its political goals — a claim firmly rejected by the movement, which calls for a cultural boycott of Israel over its policies towards Palestinians.
BDS recently called for artists to boycott the Eurovision Song Contest held in Tel Aviv last month.
“'Don't buy' stickers of the BDS movement on Israeli products remind one of inevitable associations with the Nazi call 'Don't buy from Jews', and other corresponding graffiti on facades and shop windows,” said the non-binding resolution in parliament.
Israeli Prime Minister Benjamin Netanyahu praised the resolution on Twitter as an “important decision”.
'Out of control'
Schäfer, director of the museum since September 2014, had recently had his contract extended to stay in post until August 2020, according to the museum. Schäfer came under pressure after a tweet was sent by the museum encouraging people to read an article by Jewish scholars that criticised the parliamentary resolution.
In an interview with Der Spiegel on Wednesday, Schäfer defended the tweet as a “contribution to the discussion” but acknowledged the wording used was unfortunate.
Reacting to the tweet, the president of the Central Council of Jews in Germany, Josef Schuster, criticised the museum as seeming to be “totally out of control”.
A museum statement on Friday said Schäfer “today proposed his resignation to the chairman of the board of the foundation and Culture Minister Monika Grutters to avoid further harm to the Jewish Museum Berlin”.
The spokeswoman for the museum that wrote the tweet was also dismissed for violating the neutrality rule of a publicly funded institution, the daily Suddeutsche Zeitung reported on Friday.
The museum has been repeatedly criticised by Israel for its “anti-Israeli stance”, according to the German media.
In March, Schäfer sparked uproar by welcoming the head of the cultural affairs department at the Iranian Embassy in Berlin, Seyed Ali, to his house to discuss a possible display of archival photos of Iranian Jews, reported Suddeutsche Zeitung.
Issues related to anti-Semitism and Israel remain extremely sensitive in Germany, which has a culture of atonement over atrocities committed during World War II
Anti-Semitic crimes rose by 20 percent in Germany last year, according to interior ministry data which blamed nine out of 10 cases on the extreme right.