The BBC reports that according to local officials, Oleksiy Vadatursky, 74, and his wife Raisa have died after a missile hit their home.
Mr Vadatursky owned Nibulon, a company involved in grain exports. He had also received the “Hero of Ukraine” award.
An adviser to President Zelensky’s office said he believed Russia had deliberately targeted the businessman.
Mykhailo Podolyak said one of the missiles had hit the businessman’s bedroom, adding that this left “no doubt” it had been guided.
Nibulon has built many storage facilities and other infrastructure for exporting grain.
The region’s leader, Vitaliy Kim, said Mr Vadatursky’s “contribution to the development of the agricultural and shipbuilding industry, the development of the region is invaluable”.
The two countries signed a UN-brokered agreement in Turkey last week, aimed at easing the food crisis. The deal was almost derailed by a Russian attack on the Odesa port the following day.
The resumption of Ukrainian exports has been further delayed by security checks. But on Sunday Turkey said the first ship carrying grain was expected to leave Odesa on Monday morning.
Ukraine accuses Russian forces of stealing grain from farms on occupied land and exporting it via Crimea – Ukraine’s southern peninsula annexed by Russia in 2014. Russia denies Ukrainian claims.