In a press release issued on Friday afternoon, the bank confirmed it had "submitted a notification" to Finansinspektionen after identifying "transactions that 'can be assumed to' constitute criminal offences".
"These transactions were carried out by the bank's former chief executive Michael Wolf," said the bank.
According to Swedish legislation, anyone who reports similar cases to Finansinspektionen is prohibited under a gagging order from disclosing it to third parties, including the suspect themselves.
But after Swedish business newspaper Dagens Industri (DI) broke the story on Friday, Swedbank said it had decided to confirm it in agreement with the authorities involved.
The report has been passed on to the Swedish Economic Crime Authority, which has decided to launch an investigation.
Wolf denied all accusations on Friday, blaming them on a "smear campaign".
"I am incredibly surprised at the report. I deny all allegations about criminal activity. I welcome an investigation which will prove that I am innocent. I believe, unfortunately, that this is another part of a smear campaign against me," he told the TT newswire in a written statement.
The former boss was asked to step aside by Swedbank's board of directors in a shock move earlier this week. It said at the time that it was "time for a new leadership and a new CEO who can take Swedbank to the next level".
The move followed recent media criticism of both Wolf's work and that of the bank's board. FI announced a month ago that it had launched an investigation linked to a potential conflict of interest between the internal work of senior staff members and a number of property transactions.
Wolf, who was born in 1963, joined Swedbank six years ago after previous high-profile roles at Swedish engineering giant Skandia and rival bank SEB.
He has been on a 13 million kronor ($1.53m) annual package and the bank said on Tuesday that he would receive 75 percent of his salary for the next 12 months as part of his exit deal, as well as an additional severance payment worth the same amount.
The Swede was recently ranked the ninth best executive in the world by Harvard Business Review, which looks at areas including social responsibility, governance and caring for the environment.