It was not immediately clear who would succeed her as prime minister, a job she has held since late 2017.
“I had decided some time ago not to seek re-election in the next parliamentary elections. At the same I still have a burning desire to continue to offer my services to Icelandic society,” Jakobsdóttir said in a video message.
Iceland will hold a vote on June 1 to elect its new head of state.
The island nation of almost 400,000 people faces uncertainty after
recent volcanic eruptions that triggered the indefinite
evacuation of thousands adding to pressures on an economy already facing high inflation and soaring interest rates.
Still, Jakobsdóttir said she believed the government had made significant progress on the challenges and that the country was on a firmer footing than just a few months ago.
Jakobsdóttir has been crucial in keeping together the current coalition of her own Left-Green Movement, the pro-business Independence Party and the center-right Progressive Party.
The government has been in power since 2017, providing unusual stability in a country
which went to polls five times from 2007 to 2017, a period marked by political scandals and distrust of politicians following the 2008 financial crisis.