As a result, the 2018 prize will be given in 2019 instead, the academy announced today.
The choice was made on the grounds the academy is in no form to choose a victor after the intercourse abuse allegations and monetary crimes scandals.
The Academy said the decision was made "in view of the now diminished Academy and the reduced public confidence in the Academy".
This is the first time since 1949, that the jury which handles the world's most prestigious literary awards will not announce a victor this year, but would announce two winners in 2019.
The controversies that the Swedish Academy finds itself in has shaken the Swedish establishment.
"One of the circumstances that may justify an exception is when a situation in a prize-awarding institution arises that is so serious that a prize decision will not be perceived as credible", a press statement from the foundation read. The group's regulations don't include a provision for members to quit, but that's something Sweden's King Carl XVI Gustaf (the academy's formal patron) said he plans to change because of the current crisis.
The academy's statutes require a quorum of 12 to vote in any new members.
When did this scandal start?
Arnault denies all the allegations against him, including that of being the source of leaks, his lawyer said. The academy also enlisted a law firm to investigate the academy's association with Arnault.
The Academy has cut all ties with Arnault's cultural centre Forum in Stockholm, which it had subsidised for years and which was a key meeting point for the country's cultural elite.
Arnault also has been suspected of violating century-old Nobel rules by leaking names of winners of the prestigious award - allegedly seven times, starting in 1996.
What followed was a wave of resignations, including Ms Frostenson and the head of the academy, Prof Sara Danius. Frostenson was also among the six who resigned. That has meant those who withdrew could not be replaced.
Where is this playing out?Academy members were divided about whether to stand as neutral guarantors of the arts, or as supporters of their fellow author.
What's next for the academy isn't clear, though the Swedish king has hinted change may be coming. Last year, a Swedish newspaper reported that Arnault had harassed or assaulted 18 women, and since then, more accusations have come out, including that he groped Sweden's Crown Princess, Victoria.
A plaque depicting Alfred Nobel at the Nobel Peace Prize Ceremony 2008 in Oslo City Hall on December 10, 2008 in Oslo, Norway. He was the first and only Arab from the Arab world to have been given the prize.
"The strong woman who tried to clean up the Swedish Academy was forced to leave".
The Nobel Foundation, in a statement on its own website, supported the Academy's decision to postpone this year's victor. "With this scandal you can not possibly say that this group of people has any kind of solid judgment".
There will be no Nobel prize for literature this year.
For the first time since 1943, the Nobel Prize for Literature will not be awarded this year amid a sex abuse scandal.