Bieler, one of the nationalist party’s highest profile members of parliament, said she expects to be off work for the foreseeable future.
Writing on Facebook, she said she had tried to scale back her activities “but unfortunately my well-being continued to go downwards”.
Two years ago Sweden Democrat party leader Jimmie Åkesson sparked a major surprise when he too announced he was taking a break from politics because of exhaustion.
Mattias Karlsson stood in as party leader for five months before Åkesson returned to the fray at the end of March 2015.
The party, with roots in the neo-Nazi movement, is a pariah in Swedish politics and other parties have vowed to keep it out of government.
But the Sweden’s Democrats’ popularity has propelled them into parliament and they are currently polling at 17 percent, making them the country's third largest party with two years to go until the next general election.