Two of the crew members were confirmed dead in the crash, one was critically injured and one went missing, the ministry's consular service department said in a statement on its official Facebook page, Xinhua reported.
The missing crew member was later confirmed dead, raising the death toll to three, Sadhan Kumar Mohanta, manager of Cox's Bazaar Airport from which the plane took off, said in an update.
The Ukrainian side will continue to closely monitor the investigation into the cause and circumstance of the crash, the statement from the Ukrainian foreign ministry said.
The Antonov An-26 cargo plane crashed shortly after takeoff into the Bay of Bengal off the coast of Bangladesh's southeastern Cox's Bazaar district at about 9:05 a.m.
Initial reports from the Bangladeshi police suggested that a Russian pilot was killed in the crash.