An opera house, concert hall and government offices were hit in Freedom Square, in the centre of the north-eastern city Kharkiv.
At least 20 people including a child were injured, but authorities are still trying to clarify the death toll.
The attack came as Ukraine's president said Russia was committing war crimes.
"This is the price of freedom," President Volodymyr Zelensky said. "This is terror against Ukraine. There were no military targets in the square – nor are they in those residential districts of Kharkiv which come under rocket artillery fire," he added.
Video footage showed a missile hitting the local government building and exploding, causing a massive fireball and blowing out windows of surrounding buildings. Freedom Square is the second largest city-centre square in Europe and a landmark of the city.
At least one person is confirmed to have died – an Indian student living in the city.
Kharkiv has been bombed heavily for days now, and 16 people were killed before Tuesday's attack Mr Zelensky said. His government accuses Russia of trying to lay siege to Kharkiv and other cities, including the capital Kyiv, where a huge Russian armoured convoy is approaching.
Ukraine's Foreign Minister Dmytro Kuleba said the world must do more to punish Russia for the "barbaric" attack on Freedom Square and residential neighbourhoods, accusing the Russian President Vladimir Putin of committing "more war crimes out of fury, murdering innocent civilians".
The sixth day of Russia's invasion of Ukraine has seen continued attacks on several fronts, but the Russian advance has reportedly been slowed by Ukrainian resistance.
People in the southern city of Kherson say it is now surrounded, and the mayor of Mariupol, a port city also in the south of Ukraine says it endured relentless shelling overnight.
Meanwhile new satellite images showed a 40-mile (64km) long Russian military convoy snaking its way toward the capital, Kyiv, where air raid sirens were again ringing out on Tuesday morning.
The convoy – which seems to have slowed down in the past 24 hours – includes armoured vehicles, tanks, artillery and logistical vehicles, and is said to be less than 18 miles (30km) from Kyiv.
Nato chief Jens Stoltenberg on Tuesday accused Russian President Vladimir Putin of "shattering peace in Europe", while UK Prime Minister Boris Johnson accused Russia of "barbaric and indiscriminate practises… to send missiles into tower blocks to kill children."
"Yesterday there was very intense shelling on residential areas," said Maria Avdeeva, an international security expert who is currently in Kharkiv.
"Actually, it was the first time that Russia was deliberately targeting houses with people living there," she told the BBC's Newsday programme.
"Already we have shortages… we still have water, it is running in the house. But at any moment Russia could hit the critical infrastructure facilities. There are shortages of food already. So, I think that almost nothing is left in the shops," Ms Avdeeva, who is a research director at the European Expert Association think tank, added.
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