Her resignation comes amid criticism regarding how the organization, which has picked the victor of the Nobel Prize for Literature since 1901, handled an investigation into allegations of sexual misconduct by a man married to one of its members.
This photo posted on the Instagram account of Alice Bah Kuhnke on Friday, April 13, 2018 shows the Swedish Culture minister posing for a photo in support for ousted head of the Swedish Academy.
Her resignation comes after a Swedish newspaper reported that 18 women had made allegations of harassment and physical abuse against the husband of Katarina Frostenson, a member of the Academy.
The foundation issued a statement noting that "trust in the Swedish Academy has been seriously damaged" and demanding that the group take specific actions to restore that trust.
"It is the academy's wish that I leave my post as permanent secretary", said Danius, a 56-year-old Swedish literature historian, and the first woman to hold the position.More news: Volkswagen names new boss to steer sweeping overhaul
The crisis is threatening the very institution of the Academy, since members are appointed for life.
Arnault denies the alleged assaults, which reportedly occurred between 1996 and 2017.
State prosecutors are continuing to investigate incidents related to the allegations, Reuters reports.
Sara Danius announced her decision on Thursday after a three-hour emergency meeting of academy members in central Stockholm.
Before the departures of Danius and Frostenson, seven of the academy's 18 members were women.More news: Start time changed for tomorrow's Food City 500 at Bristol Motor Speedway
Hours after Danius' announcement, the Academy said Arnault's wife, Katarina Frostenson, had also chose to quit from her post on the board.
Neither Frostenson nor the academy would elaborate.
The Academy meanwhile is conducting an internal investigation into the allegations amid fears that its global reputation and the standing of its Literature prize could be tarnished."This is devastating for the reputation of the Nobel prize", Mattias Berg, who covers cultural affairs for SR radio, told AFP.
Danius' leadership was undermined by her predecessor, who challenged her handling of a case of sexual abuse, conflict of interest, and the leaking of Literature Prize winners.
Sweden itself saw thousands of sexual misconduct allegations surfacing. "Now it is enough, we refuse to go back", Bah Kuhnke said.More news: Indian Premier League on Sky Sports Cricket - today's action