Magdalena Andersson, was announced as leader on Wednesday but resigned after her coalition partner quit the government and her budget failed to pass.
Her coalition partner, the Greens Party said it could not accept a budget "drafted for the first time with the far-right".
Ms Andersson said that she hoped to to try to become prime minister again as a single party government leader.
"There is a constitutional practice that a coalition government should resign when one party quits," the Social Democrat said on Wednesday.
Ms Andersson was elected as prime minister earlier on Wednesday because under Swedish law, she only needed a majority of MPs not to vote against her.
Becoming the first woman prime minister in Swedish history should have been cause for a night of celebration for Magdalena Andersson, yet the sun had barely set when she handed in her notice.
If there's another prime ministerial vote, Ms Andersson will probably get voted in again.
This is because the Green party has promised to support her, despite quitting as a formal coalition partner.
But she'd end up in a vulnerable position at the helm of a fragile minority government, and would still have to stick to the right-wing budget already voted on by parliament.