Four children are among those injured.
"Odesa: another night attack of the monsters,” Oleh Kiper, governor of the region said on Telegram.
“Unfortunately, we have one civilian killed as a result of the night time terrorist attack by Russians on Odesa," he added.
Later on Sunday morning conflitcing reports suggested a second person had been killed but at the time of writing, the official death toll remains one.
"A man born in 1974 was killed in the night time shelling," Igor Klymenko, Ukraine's minister of internal affairs, said on Telegram.
"Twenty-two people were injured. Among them are four children: 11, 12, and two 17-year-olds."
On Sunday morning, President Zelensky vowed retaliation against "Russian terrorists."
"Missiles against peaceful cities, against residential buildings, a cathedral... There can be no excuse for Russian evil.
"As always, this evil will lose. And there will definitely be a retaliation to Russian terrorists for Odesa. They will feel this retaliation."
Missiles against peaceful cities, against residential buildings, a cathedral... There can be no excuse for Russian evil. As always, this evil will lose. And there will definitely be a retaliation to Russian terrorists for Odesa. They will feel this retaliation.— Volodymyr Zelenskyy / Володимир Зеленський (@ZelenskyyUa) July 23, 2023
All those who… pic.twitter.com/gcpD30BFP1
The attack – which used 19 kalibr, Onyx, Kh-22, Iskander-K, and Iskander-M ballistic missiles – also damaged the city’s largest cathedral.
Ukraine’s armed forces said nine of the missiles were intercepted, adding: “The rest caused destruction to the port infrastructure, at least six residential buildings, including apartment blocks.
“Dozens of cars, facades and roofs in many buildings in the city were damaged, windows were broken. On one of the central squares of Odesa, the cathedral of the Ukrainian Orthodox Church (Moscow Patriarchate) was damaged by a Russian missile.
“Two architectural monuments were harmed.”
The head of Ukraine's presidential office, Andriy Yermak, repeated Kyiv's call for more missiles and defence systems after the attack on Odesa.
“The enemy must be deprived of the ability to hit civilians and infrastructure. More missile defence systems, as well as ATACMS -- this will help Ukraine," he said on Telegram, referring to the long-range tactical missiles that Kyiv wants Washington to supply.
In a video filmed from the scene of the ruined cathedral, Ukrainian MP Oleksiy Goncharenko, said: "I address this to the world – Odesa needs protection. This is the port where grain facilities work to feed 400m people, 400m people who are reliant on Ukrainian crops.
"Russia is absolutely and deliberately destroying it. We need protection and we need air defenses right now."
Right now I'm in an Orthodox Cathedral that was destroyed by Russian missiles today in Odesa!— Oleksiy Goncharenko (@GoncharenkoUa) July 23, 2023
Odesa needs protection! We need more air defense right now! pic.twitter.com/ojj5ZoSzAI
Odesa has been bombed several times since the start of the invasion, and in January the United Nations cultural agency UNESCO designated the historic centre of the city as a World Heritage in Danger site.
The city has come under repeated attack since Moscow pulled out of a grain export deal last week.
Ukraine has accused Russia of targeting grain supplies and infrastructure vital to the Black Sea deal.
Moscow said Sunday it hit all intended targets in Ukraine's port city Odesa port, claiming the sites were being used to prepare "terrorist acts" against Russia.
"At night the armed forces of the Russian Federation caried out a strike... on facilities where terrorist acts against the Russian Federation using unmanned boats were prepared," the Russian army said.
"All planned targets in the strikes were destroyed."
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