Russian forces used guided bombs in the attack, news outlets reported.
Ukraine's President Volodymyr Zelensky said a 14-year-old girl was among the dead.
Kharkiv Mayor Ihor Terekhov had earlier said that one child was killed in the playground.
The 12-storey residential high-rise caught fire as a result of the strike, the mayor said.
The casualty toll from the attack was expected to rise as rescuers dug through the rubble for survivors or bodies, authorities said.
Some of the injured were in severe condition, according to regional governor Oleh Syniehubov.
'We need strong decisions from our partners to stop this terror': Zelensky
Zelensky renewed his appeal to Western allies to allow Ukraine to use long-range weapons to attack Russian military air bases.
He said on social media that the Russian strike on Kharkiv was "carried out using a Russian guided aerial bomb—a strike that could have been prevented if our Defense Forces had the capability to destroy Russian military aircraft at their bases."
Zelensky added: "We need strong decisions from our partners to stop this terror. This is an absolutely legitimate need. There is no rational reason to limit Ukraine’s defense. We need long-range capabilities and the full implementation of air defense agreements for Ukraine. These are life-saving measures."
Kharkiv, Ukraine's second-largest city, lies about 30 kilometres from the border with Russia.
The city, which is home to around 1.3 million people, has frequently been targeted by Russia since it invaded Ukraine more than 30 months ago, the Reuters news agency has reported.
Russia invaded Ukraine on February 24, 2022, starting the largest armed conflict in Europe since World War II.
Friday is day 919 of Russia’s war on Ukraine.
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Source: IAR, PAP, Reuters, ukrinform.net
