Interior Minister Anders Ygeman, a political heavyweight in the centre-left government who reportedly knew about the leak but failed to inform the premier, will quit "at his own request", Lofven told a press conference, adding that Infrastructure Minister Anna Johansson will also step down.
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The scandal has blown up in recent weeks after it emerged that an entire database on Swedish drivers' licences was made available to technicians in the Czech Republic and Romania, with media reporting that the identities of intelligence agents may have been jeopardised.
Defence Minister Peter Hultqvist has kept his job - which was also on the line over one of the largest breaches of government information in Sweden in decades - but still faces the threat of being forced out in a censure motion launched by the opposition on Wednesday against all three ministers.
Opposition parties have yet to confirm whether the motion will now go ahead. Lofven, at the head of a Social Democrat-led coalition since 2014, did not announce snap elections as had been expected by political commentators after the scandal, instead saying he intends to stay on until his term ends in 2018.
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"I have no intention of plunging Sweden into a political crisis," he said, pointing to "formidable challenges" the country is facing including tensions in the Baltic region, Brexit, and the government's plans for social and economic reforms.
"I looked at several alternatives, and I chose the best one for the country," Lofven said.
The data leak stems from the Swedish transport agency's hiring of IBM in 2015 to take over its IT operations. IBM in turn used subcontractors in the Czech Republic and Romania - making the sensitive information accessible by foreign technicians who did not have security clearance.
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