But Prime Minister Stefan Lofven vowed he would be staying on despite speculation he could call a snap election.
Interior Minister Anders Ygeman, a political heavyweight previously seen as a likely future prime minister, has resigned, Lofven said at a press conference, adding that Infrastructure Minister Anna Johansson will also step down.
Ygeman reportedly knew about the leak from the national transport agency, which made the private data of millions of citizens accessible abroad, but failed to tell the prime minister.
Lofven's Social Democrat-led minority government has been badly rattled by one of Sweden's largest data breaches in decades, and opposition parties had threatened the coalition with a vote of no confidence.
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Some political commentators had expected Lofven to call an early election at today's press conference -- but he said he intends to serve his full term, which ends in 2018.
"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.
Swedish Defence Minister Peter Hultqvist kept his job in the reshuffle despite facing claims that, like the interior minister, he knew about the scandal but failed to tell the premier.
However, Hultqvist still faces the threat of being forced out in a censure motion launched by the opposition yesterday against all three ministers caught up in the scandal.
"The prime minister will not take responsibility, which is why we will hold him to account in parliament."
The far-right Sweden Democrats signalled they would support the censure motion, which would need a parliamentary majority to remove Hultqvist from office.
According to Helle Klein, editor-in-chief of the daily Dagens Arbete, a left-wing newspaper affiliated with unions, Sweden's centre and right wing parties that make up "the alliance" are engaging in "distasteful power games".
Maria Agren, head of the transport agency at the centre of the leak, quit in January for undisclosed reasons but has since confessed to violating data handling. She accepted a fine of 70,000 Swedish kronor (around USD 8,000).
Johansson, who oversees the transport agency, said her former state secretary had known about the leak but kept the information hidden from her -- triggering heavy criticism among opposition parties who said she should have known what was happening.