Her family told Swedish news agency TT that Danius, a literary scholar, critic and author, passed away early Saturday following a long illness.
Swedish media said she had breast cancer.
Danius was elected to a lifetime position on the Swedish Academy's board in 2013 and because the body's first female permanent secretary in 2015. She resigned the position in 2018.
The Stockholm University professor published a book last year about singer-songwriter Bob Dylan after playing a central role in the Swedish Academy's decision to make him a Nobel laureate in 2016.
"Everything she did was characterized by a rare strength and luminosity," read a brief obituary on the Swedish Academy's website Saturday.
Sweden's King Carl XVI Gustav said he was sad to hear of Danius' death. The monarch, who is the academy's patron, said they held regular meetings with "interesting conversations" during her time there.
"A strong cultural figure has left us, way too early," Carl XVI Gustav said in a statement.
Danius resigned as head of the prestigious institution in early 2018 after an internal dispute grew into a sexual misconduct and financial crime scandal that aroused concerns in the king and brought criticism from the Nobel Foundation's board.
Danius wasn't accused of personal wrongdoing. When she stepped down as permanent secretary, she said her academy colleagues had lost confidence in her leadership and acknowledged the internal turmoil had "already affected the Nobel Prize quite severely."
The Swedish Academy didn't award the literature prize last year so named two winners - one for 2018 and one for 2019 - on Thursday.