Russia struck the Black Sea city on Monday, also injuring almost two dozen.
"Unfortunately, the number of victims in yesterday's Russian missile attack on Odesa increased to five people," the head of the Odesa region Oleg Kiper said on social media.
He said the toll climbed after a man born in 1960 died in hospital.
Kiper said 23 wounded people were still undergoing medical treatment.
"Eight are in serious condition, four of them in an extremely serious condition, including a four-year-old girl," he said.
"Our doctors are trying to do their best," he added.
Separately, the head of the southern Kherson region said Russian shelling killed one person in the last 24 hours.
Russia has hit Ukrainian cities for months relentlessly and rushed a push on the front in eastern Ukraine ahead of the arrival of crucial US weapons to Kyiv.
Moscow's invasion of Ukraine has dragged on for 26 months.
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