Kjærsgaard confirmed the conclusion of her spell as speaker on social media.
“Thank you and goodbye to the position as speaker of parliament. Many have asked since the election whether I will continue as speaker. I will not. Power has shifted,” she wrote on Facebook.
“I have held this honourable position for four years and have enjoyed every day. We should all be proud of our well-functioning representative system,” she added.
Kjærsgaard, who led the anti-immigration DF from 1995 until 2012, was re-elected in the vote last week, and will continue to represent in parliament her party, which was reduced from 37 to 16 seats.
The Christiansborg legislature had been expected to select a new speaker following the election, since a majority is required to vote for the speaker.
That support was unlikely to be given to the occasionally outspoken Kjærsgaard, with the left-of centre ‘red bloc’ of parties now holding more than half of the seats in parliament.