The bank and its founder Mohammad Yunus, who shared the 2006 Nobel prize with the institution, are suspected of diverting money from Norwegian state development agency NORAD from one project to another.
"We will review the management of foreign funded micro-credit schemes by the Grameen Bank and report back to the government in three months' time," Monowar Uddin Ahmed, head of a five-member investigation team, told DPA Wednesday.
The probe was announced in December, and formally launched Tuesday.
Criticism of the bank came to light after a Norwegian documentary in November alleged the bank transferred $100 million provided by NORAD and other donors to Grameen Kalyan, another of its ventures, in 1996, without respecting procedures laid down by the donors.
In December 2010, Yunus said that he had received no undeclared benefits from Grameen, and that there was no question of corruption in the organisation.
The matter regarding the diversion of money via the bank's so-called revolving funds was "an honest disagreement between GB (Grameen Bank) and NORAD, but never prompted by any dishonest intention," he was quoted as saying by Bangladeshi daily the Financial Express.
He also said that an investigation by the Norwegian authorities found no evidence of a breach of its rules.
But Prime Minister Sheikh Hasina has accused Yunus, who briefly set up his own political party in 2007, of using "tricks" to avoid taxes, and "sucking blood from the poor" with his bank's loans.
The Grameen Bank is widely regarded as the pioneer of micro-finance, which consists of lending very small amounts to the poor at rates slightly higher than other banks.
The system, originally praised for reaching those excluded from normal commercial credit, has come under criticism in recent years for encouraging debt and taking excessive profits.