Oleksiy Vadatursky, 74, and his wife Raisa died when a missile hit their home overnight, Ukrainian media said.
Vadatursky owned Nibulon, a group involved in grain exports. He had also received the "Hero of Ukraine" award.
Mykolaiv mayor Oleksandr Senkevych said it was probably the heaviest Russian bombardment of the city so far.
There was damage to a hotel, a sports complex, two schools and a service station, as well as homes.
Mykolaiv is on the main route to Odesa, Ukraine's main port, and has been hit repeatedly.
The region's leader Vitaliy Kim said Vadatursky "did a lot for the Mykolaiv region, a lot for Ukraine.
"His contribution to the development of the agricultural and shipbuilding industry, the development of the region is invaluable," he said on Telegram.
Nibulon has built many storage facilities and other infrastructure for exporting grain.
Ukraine and Russia are major exporters of wheat and other grains, and the disruption of exports caused by the war has sent food prices soaring worldwide.
The two countries signed a UN-brokered agreement in Turkey last week, aimed at easing the food crisis.
The resumption of Ukrainian exports has been 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. Russia denies those claims.
Meanwhile, Russia has canceled Navy Day celebrations in occupied Crimea.
The reason given by Sevastopol Governor Mikhail Razvozhayev was an alleged Ukrainian drone strike on the Black Sea Fleet headquarters. The fleet has long been based in Sevastopol.
But a senior Ukrainian official Serhiy Bratchuk dismissed the Russian report as a "provocation".
"The liberation of our Crimea will take place differently and much more efficiently," he said.
Russian forces annexed Crimea in 2014. That was internationally condemned as illegal and triggered sanctions against Russia.
Navy Day is an annual Russian holiday, and celebrations are taking place across Russia on Sunday. President Vladimir Putin is overseeing events in St Petersburg, his home city.
In a Telegram post, the Sevastopol governor said "an unidentified object flew into the courtyard of the [Black Sea] Fleet headquarters" and "according to preliminary data, it was a drone".
Blaming "Ukronazis", he said six people — Fleet HQ staff — were wounded, and none were killed.
Russia has often accused Ukrainian authorities of being "Nazis", as part of the Kremlin's propaganda campaign to justify its invasion of Ukraine on Feb. 24.
A photo posted by Governor Razvozhayev showed him in a courtyard littered with leaves, but with no obvious structural damage. He said the Navy Day celebrations had been canceled for security reasons.
In a previous blow to the Black Sea Fleet, in April, the fleet's flagship Moskva sank after what Ukraine described as a strike with two Neptune missiles.
Russia admitted there was a big fire on board caused by exploding ammunition, without attributing it to a Ukrainian attack, and said the missile cruiser sank in a storm while being towed.
It remains unclear how many Russian sailors were killed or injured in the ship's demise.
Meanwhile in the north, Ukraine's second city Kharkiv was hit by Russian missiles again, mayor Igor Terekhov said on Telegram. Three Russian S-300 missiles struck a school there, destroying the main building, he said.
The BBC was unable to verify the latest reports independently.
In a late-night address on Saturday, Ukraine's President Volodymyr Zelenskyy told all civilians still living in parts of eastern Donetsk region under Ukrainian control to evacuate.
The region has seen heavy clashes amid a slow advance by Russian forces, who already control large parts of it.
"The more people leave Donetsk region now, the fewer people the Russian army will have time to kill," Zelenskyy said. "We will use all available opportunities to save as many lives as possible and to limit Russian terror as much as possible."