The money was sent from the All-Russian Regional Development Bank in three multimillion-dollar transfers to Belarus in 2011 and 2012, RIA Novosti reported Friday.
The transfers allegedly paid for imported foreign goods.
Approximately 85 percent of the bank, the 78th largest in Russia, is owned by Rosneft, an oil company lead by Igor Sechin, a government official when Vladimir Putin was prime minister.
In announcing the investigation, an Interior Ministry spokesman said the criminal case is "not against the bank or its employees but in relation to unnamed clients of the bank."
No arrests have been made and police say they have no official suspects.
A bank source said Rosneft has no connection to the alleged money laundering, ITAR-Tass reported.
The bank has 20,000 clients, the source said.
Belarusian imports and exports are hard for Russian banks to track because of the country's membership in a customs union with Russia.
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club
Theater accidentally screens 'Nymphomaniac' trailer instead of Disney's 'Frozen'