The regulator said Klarna had "significant deficiencies" in its general risk assessment, failing to assess how the bank's products and services could be used for money laundering or terrorist financing.
"It is important to counteract the risk that the firm's operations could be used by criminals," the regulator, Finansinspektionen (FI), said in a statement.
The bank is known for its "buy now, pay later" service which allows shoppers to pay up to 30 days after placing an order or making purchases in four instalments without interest.
FI said it had investigated Klarna between April 1st, 2021 and March 31st, 2022.
Klarna said it may appeal the decision.
"It's too early to say, we need to go through (the decision) first," Klarna spokesman Joel Hedin told AFP.
"It is important to emphasise that the decision concerns rule interpretation and application and not actual cases of money laundering," he said.
"We have had a constructive dialogue since the investigation began ... and see this as an important part of the joint work for a secure financial sector," he said.
The company noted on its website that the banking industry "navigates a complex set of regulations, which is also demonstrated by the fact that all other major (Swedish) banks have received reprimands within the framework of the money laundering regulations".
Klarna was recently valued at $14.6 billion in an accounting transaction by one of its shareholders, the British fund Chrysalis, Bloomberg reported.
The company announced in November it had taken the first steps towards an initial public offering (IPO) in the United States.
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