Four adults and five children had been wounded, he added, without specifying their condition or if they had been in the residential building.
He did not give details on the strike.
Earlier, Ukraine’s air force had announced an air alert for Mykolaiv and Odesa, around 100 kilometers (60 miles) away and several other regions.
It said it had detected the launch of “missiles” towards the Odesa region.
“There is a huge hole in the ground near a three-story residential building,” Mykolaiv mayor Oleksandr Senkevych wrote on Telegram.
Emergency services were working at the site, he said.
“At least five residential high-rise buildings” had been damaged, he said.
At another address “about 15 garages” were damaged, he said, without giving details.
The city of Odesa had been attacked, regional governor Oleg Kiper wrote on Telegram, without specifying the nature of the attack.
“As a result of the Russian attack, there is destruction in the center of Odessa,” he said.
Authorities had information on “two hospitalized victims,” he said, without giving details.
Ports in Odesa were key transit hubs for the export of grain from Ukraine until Moscow said earlier this week it would withdraw from a deal giving safe passage to cargo ships in the Black Sea.
Kyiv on Wednesday claimed Russia had destroyed 60,000 tons of grain meant for export in overnight strikes around Odesa.
Mykolaiv is located on the Black Sea, about 170 kilometers (100 miles) from Moscow-annexed Crimea. Russian forces have frequently targeted it since Moscow launched its invasion in February 2022.
On Tuesday governor Kim said an “industrial facility” in the city was hit in an overnight attack launched hours after the Kremlin refused to extend the grain export deal.