CID Special Superintendent of Police Molla Nazrul Islam told bdnews24.com his department received a report from the central bank on the transactions by 2,887 bKash agents earlier in the day.
"We will investigate the transactions," he said.
bKash Limited Head of Corporate Communications Shamsuddin Haider Dalim told bdnews24.com they have not received instructions from the central bank.
"We will act once we get instructions," he said.
bKash, a joint venture of BRAC Bank, US-based Money in Motion, International Finance Corporation of World Bank Group and Bill and Melinda Gates Foundation, was launched in 2011.
Around 70 percent of Bangladesh's mobile money transfers take place through bKash. A huge part of the mobile banking agents across the country belong to the company.
Central bank Director Saha said the process to check transactions by agents of other mobile banking service providers was under way.
He said irregularities found in inspections by Financial Intelligence Unit, Bangladesh Bank's study on decreasing inflow of remittance, information given by bKash, complaints received from different sources, and information given by law-enforcing and intelligence agencies have been analysed to make the list of 'irregular' transactions.
A CID official said these agents under investigation had not followed Bangladesh Bank's instructions in making the transactions.
The timing of the transactions was also 'suspicious', he added.
The Bangladesh Bank report said some of the agents had opened different individual accounts using same identity cards.