The whale carcass washed up on a beach near the port city of Chittagong, 217 kilometers (135 miles) southeast of the capital, Dhaka, Marine Fisheries Department official Mohammad Faruk said.
"Local fishermen initially thought it was wreckage from a grounded ship," Faruk said.
It was not clear what species the whale belonged to or how it died.
A team of experts was expected to visit the site Tuesday, Faruk added.
The tail and fins of the whale, meanwhile, appeared to be mutilated, private television channel ATN Bangla said.
Migrating whales are sometimes sighted in the Bay of Bengal off Bangladesh's southern coast, but rarely come near shore, experts and witnesses say.
The choice of the city of Helsinki is not incidental as the capital of Finland had hosted US-Soviet negotiations on the limitation of nuclear stockpiles in 1969