It is the first European government to collapse due to its handling of the pandemic but the move will keep the current four-party coalition in power and avoid the possibility of an early election.
Slovak Prime Minister Igor Matovic has resigned following heavy criticism in the ex-communist country of his decision to buy Russian vaccines and of his handling of the coronavirus pandemic in general.
President Zuzana Caputova nominated Finance Minister Eduard Heger to replace him at a ceremony involving all three politicians in the capital Bratislava that was broadcast live on Slovak television.
"When one year takes ten years of your life ... It was an honour and thank you," Matovic wrote on Facebook before the ceremony.
As it battles one of the highest Covid death rates in the world, Slovakia has been stuck in a political crisis ever since Matovic staged a press conference in front of a delivery of Sputnik V vaccines on March 1.
Matovic, a former businessman in the publishing industry, came to power last year after beating the governing populists on an anti-corruption platform.
While supporters viewed him as a maverick with a knack for self-promotion, critics accuse Matovic of being an unpredictable, attention-seeking control freak.
He has said he would like to stay on in the cabinet as the new finance minister but some coalition allies want him to be out of the government entirely.
During the pandemic in Slovakia, a eurozone country of 5.4 million people, Matovic's critics have accused him of poor communication and political missteps.
But his decision to buy Sputnik V vaccines has proved particularly divisive, with the former foreign minister Ivan Korcok calling the jabs "a hybrid war tool".
Heger, like Matovic a former businessman and member of the OLaNO party, is seen as a political pragmatist.
Bratislava-based political analyst Pavol Babos said he was "less emotive" than Matovic but still loyal to him.
However, analysts say his deeply held Christian views could create tensions with liberals in the coalition.
The 44-year-old will now have to build consensus within the four-party grouping in the coming days before seeking the approval of parliament in a confidence vote.
He is expected to introduce his nominees for the new government to Caputova later on Tuesday.
According to local media, most of the ministers serving in the current cabinet are expected to return, including those who resigned in the past few weeks as the political crisis escalated.