Kraken, one of the world’s largest cryptocurrency exchanges, is under federal investigation, suspected of violating U.S. sanctions by allowing users in Iran and elsewhere to buy and sell digital tokens, according to five people affiliated with the company or with knowledge of the inquiry.

The Treasury Department’s Office of Foreign Assets Control has been investigating Kraken since 2019 and is expected to impose a fine, said the people, who declined to be identified for fear of retribution from the company.

Kraken, a private company valued at $11 billion that allows users to buy, sell or hold various cryptocurrencies, has previously faced regulatory actions.

That same year [2019], O.F.A.C. began investigating Kraken, focusing on the company’s accounts in Iran, the people familiar with the investigation said. Kraken’s customers have also opened accounts in Syria and Cuba, two other countries under U.S. sanctions, the people said.

Mr. Powell co-founded Kraken in 2011 and was an early proponent of Bitcoin, a digital currency that was marketed as being free of any government’s influence or regulation.