"I will shortly -- probably this week -- present my resignation to President Milos Zeman," Sobotka said.
Sobotka said his abrupt decision was a way "to free the hands of coalition parties so they can launch negotiations on a solution to the situation or agree on the organisation of earlier elections."
He also made it clear that his cabinet would go with him.
"It is unacceptable for Andrej Babis to stay on as finance minister," Sobotka said, amid allegations of conflict of interest over the tycoon's business activities.
Last week Sobotka asked Babis to clarify his past use of some 55 million euros ($60 million) worth of tax-free bonds in connection with his farming conglomerate Agrofert -- an incident that has raised questions about possible tax evasion.
"Everyone must play by the rules. Minister Babis is embroiled in a massive conflict of interest," Sobotka told reporters.
Ranked by Forbes as the Czech Republic's second-wealthiest citizen, the 62-year-old Babis has denied any wrongdoing, and labelled Sobotka's decision "absolutely tragic" and "desperate."
"I have always acted in line with the law," Babis said Tuesday, calling Sobotka "a coward."
He has also claimed that Interior Minister Milan Chovanec, a member of Sobotka's social democrat party (CSSD), ordered police to investigate his business dealings, an allegation the minister has denied.
Babis's centrist ANO party is riding high in opinion polls, scoring 33.5 percent support compared with just 16 percent for the CSSD, in a survey conducted by the pollsters CVVM in April.
Caught off guard
Sobotka has been in office since 2014, with his leftist CSSD sharing power in a three-member coalition government with ANO and the smaller centre-right KDU-CSL Christian Democratic parties.
The next general election is scheduled for October 20-21, three months ahead of a direct presidential poll.
Analysts were caught off guard by Sobotka's resignation but said an early election was unlikely to be called during the summer.
"The prime minister has realised that voters see him as a competent yet weak politician," Jiri Pehe, an independent analyst, told AFP.
"Now it's up to President Milos Zeman to take the reins."
Presidential spokesman Jiri Ovcacek declined to comment. Under the Czech constitution, there is no deadline for the president to accept the government's resignation.
"The president might let the outgoing cabinet complete its mandate or he may appoint an interim cabinet of technocrats," Pehe said.
Another option is a two-party cabinet that would govern until October without ANO, he added.
Over the last week Czech media reports had been rife with speculation that Sobotka, 45, was poised to sack Babis.
"If I had proposed he be dismissed, I would have turned him into a martyr," said Sobotka, quipping that Babis had been "working hard to get ready for this role for several days."
Babis ran the sprawling Agrofert conglomerate before putting his assets into a trust earlier this year to ward off any allegations of conflicts of interest.
The farming and chemicals giant includes over 250 companies and employs 34,000 people, with an annual turnover of 6.18 billion euros. According to Forbes, Babis is worth about 2.6 billion euros.
Agrofert also controls the Mafra media group, which owns the major Czech dailies Dnes and Lidove Noviny as well as the popular Impuls radio station.
Babis is the country's most popular politician, with a 56 percent approval rating, according to the April survey by CVVM, compared with 39 percent for Sobotka, who was ranked sixth.
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