Ties between the South Asian neighbours, who have strong trade and cultural links, have become fraught since Hasina was ousted following violent protests against her rule and she took refuge across the border.
Dhaka's request to New Delhi on Monday came two weeks after India's foreign secretary visited Bangladesh and the two countries said they hoped to clear the clouds and pursue constructive relations.
"We sent a note verbale to the Indian government saying that the Bangladesh government wants her (Hasina) back here for judicial process," Touhid Hossain told reporters, referring to diplomatic correspondence between the two countries.
Hossain did not elaborate on the judicial process.
India's foreign ministry and Hasina's son, Sajeeb Wazed, did not immediately respond to requests seeking comment.
"We confirm that we have received a note verbale from the Bangladesh High Commission today in connection with an extradition request. At this time, we have no comment to offer on this matter," the official spokesperson of India's Ministry of External Affairs said.
The head of Bangladesh's interim government, Nobel laureate Muhammad Yunus, has demanded that India send Hasina back so that Bangladesh can try her for what it says are crimes against protesters and her opponents, and crimes she is accused of committing during her tenure over the past 15 years.
Authorities in Bangladesh want former prime minister Sheikh Hasina to face justice. (AP PHOTO)
Yunus has also been upset with Hasina for criticising his administration from New Delhi.
Hasina faces numerous charges, including crimes against humanity, genocide, and murder, among others. She denies the charges.
Indian Foreign Secretary Vikram Misri visited Dhaka this month and reiterated India's commitment to pursuing a constructive relationship with Dhaka.
New Delhi has said that Hasina came to India at a short notice for "safety reasons" and continues to remain here, without elaborating.
