Mohammad Jashim, a police officer who read out the complaint, said: "The case alleged that Hasina compelled the management of a private power plant to pay the amount in phases from 1998 to 2001, otherwise threatened to stop the operation of the company."
Tajul Islam had a stake in the power plant, though further details of his involvement were not immediately available.
Hasina was prime minister of Bangladesh from 1996 to 2001, when she was defeated by her rival, Begum Khaleda Zia, chief of the Bangladesh Nationalist Party.
State of emergency
The army-backed interim government currently in power imposed a state of emergency in January and has since arrested about 160 people for corruption and extortion.
They included Khaleda's eldest son and dozens of former ministers and political leaders.
On Saturday, Hasina called the interim authority headed by Fakhruddin Ahmed, a former central bank governor, "undemocratic and unconstitutional".
Her comments came after ATM Shamsul Huda, chief election commissioner, said it may take up to 18 months to complete a flawless voters' roll for the next election.
Hasina said that was too long for the country to wait.
She left Bangladesh last month and was expected to return soon, but a Dhaka newspaper said on Monday that she might stay in the United States until June.