"He passed away on November 28," the Academy said in a statement.
Ahnlund, an author, critic, translator and professor, was appointed a member of the Academy in 1983.
The 18 members of the Swedish Academy are elected for life. His successor on "chair number 7" will be elected at a later date.
In 1996, Ahnlund and two other members had a falling out with the institution's then-permanent secretary Sture Allen who refused to condemn Iran's fatwa against Indian-born British author Salman Rushdie on behalf of the Academy.
Ahnlund was at the time one of the five members of the Academy's Nobel Literature Prize committee. After that, he refused to take part in the Academy's work until his death.
In 2005, he symbolically resigned from the Academy to protest against the awarding of the Nobel Literature Prize to Austrian writer Elfriede Jelinek in 2004.
The Swedish Academy was founded on April 5, 1786, to protect and promote the Swedish language.
Each year, the members of Nobel committee present their proposals to the entire Academy, who then vote in October. The laureate must win more than half of the votes cast.
This year, the Nobel Literature Prize went to Chinese author Mo Yan.