The strike came just hours before President Zelensky fired Air Force Commander Lieutenant General Mykola Oleshchuk.
Kharkiv, Ukraine's second-largest city, lies about 35 kilometers (22 miles) from the Russian border and has been a frequent target of attacks since Russia's full-scale invasion in February 2022.
Regional governor Oleg Sinegubov said in a Telegram message that at least 59 people were injured, 20 in critical condition and some required amputations. He also said nine children were injured in the strike.
Additional photos showed part of the building's exterior wall collapsed and numerous vehicles outside the building were on fire.
Mr. Sinegubov said the airstrikes began in the Belgorod region of Russia, just across the border.
“Let's say we assume that the missile had a guidance system. We can conclude one thing,” he said.
“This street is just a park with a large crowd of citizens. This is a residential building. This is another mass terror attack on our citizens.”
President Zelensky said Russia targeted “ordinary” people and that the attacks could have been prevented if Ukraine had “the ability to destroy Russian military aircraft at their bases.”
“This is an absolutely legitimate need. There is no rational reason to limit Ukraine’s defense,” he said.
Ukraine's Western allies have partially refused to allow Ukraine to use weapons to attack Russian territory, fearing an escalation in the conflict.
Britain has allowed much of the equipment it supplies to be used against Russia, but has made an exception for the long-range Storm Shadow missile.
In May, the United States allowed Ukraine to strike targets inside Russia, but only near the Kharkiv region, and ordered it to “react only to Russian forces attacking or preparing to attack.”
Russia continues to refuse permission to conduct air strikes deep into Russian territory.
“We need long-range capabilities for Ukraine and full implementation of the air defense agreement. These are life-saving measures,” President Zelensky said.
In response to Friday's attack, U.S. Ambassador to Ukraine Bridget Brink said: “Our thoughts are with the people of Kharkiv as rescue efforts continue.
“Russia must be held accountable for these war crimes.”
Earlier this week, multiple sources told the BBC that Western technology and finance were helping Ukraine launch hundreds of long-range attacks on Russia using Ukrainian-made drones.
Targets included air force bases, oil and ammunition depots, and command posts.
