"The ship came under attack and one engineer was killed," Pijush Dutta, executive director of Bangladesh Shipping Corp, told Reuters.
"It was not clear whether it was a bomb or missile or which side launched the attack. The other 28 crewmen are unharmed," he said, without providing further details.
The Bangladesh-flagged Banglar Samriddhi had been stuck in the port of Olvia since Russia's invasion of Ukraine began on February 24 and was hit by a missile on Wednesday evening, a Bangladeshi foreign ministry official said earlier on Thursday.
In the Bangladeshi capital Dhaka, the Russian embassy said in an English-language statement on its Facebook page that the circumstances of the incident were "being established".
"We express deep condolences to the near and dear ones of the deceased. The Russian side bends every effort to ensure safe departure of the Bangladeshi ship from the port," it said.
Videos on social media showed crew members asking for help after the ship was hit.
In one video, the vessel's second engineer said the ship had been hit by a rocket with one crewmate already dead.
"We have no power supply. Emergency generator power supply is running. We are on the verge of death. We have not been rescued yet. Please save us," the seafarer said.
In another video, another crew member called Asiful Islam Asif said: "Please rescue us."
Bangladesh Shipping Corp's Dutta said he was aware of the videos, declining further comment.
Many shipping companies have suspended sailings to affected Black Sea ports and other terminals in Ukraine, with insurance premiums for voyages soaring in recent days.
At least three commercial ships have been hit by projectiles since February 24.
Russia has called its actions in Ukraine a "special operation".
