Russian forces used guided bombs in the attack, news outlets reported.
Kharkiv Mayor Ihor Terekhov said at least four explosions were heard in a densely populated residential area in the afternoon, leading to civilian deaths and injuries.
Rescue teams were working on the site of the attack, Ukrainian state news agency Ukrinform reported.
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 nearly 28 months ago, the Reuters news agency reported.
Russia invaded Ukraine on February 24, 2022, starting the largest armed conflict in Europe since World War II.
Saturday is day 850 of Russia’s war on Ukraine.
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Source: IAR, PAP, Reuters, ukrinform.net