Bangladesh High Commissioner in New Delhi Syed Muazzem Ali had met Foreign Secretary S Jaishankar last week and discussed the issue of Rohingyas in detail.
"An Indian aircraft will carry the first consignment of humanitarian assistance tomorrow...It will land at Chittagong airport at 11 am," an Indian High Commission spokesman told Press Trust of India.
Indian High Commissioner in Dhaka Harsh Vardhan Shringla would hand over the relief materials to Bangladesh's Road Transport and Bridges Minister and Awami League general secretary Obaidul Quader, the spokesman added.
Bangladesh, which is facing a big influx of Rohingyas from Myanmar, has called on the international community to intervene and put pressure on Myanmar to address the exodus.
According to the UN estimates, over 379,000 Rohingya Muslims have fled Myanmar's Rakhine state into Bangladesh since August 25 when fresh wave of violence erupted.
According to media reports, the violence began when Rohingya militants attacked police posts in Myanmar's northern Rakhine state.
Rohingya residents - a stateless mostly Muslim minority in a Buddhist-majority nation - allege that the military and Rakhine Buddhists responded with a brutal campaign against them, according to the reports.
Bangladesh had earlier said the new influx of Rohingya refugees is an unbearable additional burden on the country which has been hosting around 400,000 Myanmar nationals who had to leave their country in the past due to communal violence and repeated military operations.
Mr Quader had said on Sunday that Bangladesh needed "crucial" Indian support in handling the crisis.
"The entire world today is worried with the Rohingya issue (and) their (India's) concern and stand beside us is very crucial at this moment," he had said.
Foreign Minister A H Mahmood Ali, at a media briefing on the same day, however, referred to the Indian concern about the crisis.
A "deeply concerned" India last week asked Myanmar to handle the situation in the Rakhine state with "maturity and restraint" while focusing on the welfare of the civilian population along with that of the security forces and asserted that it was imperative that violence ends there.