At least 35 other people were injured after Russian forces dropped two bombs near a supermarket, leading to a large fire.
A nearby educational institute and high-rise building were also damaged in the attack.
The Kharkiv Regional Prosecutor's Office shared photos of the aftermath on its Telegram channel.
"A large number of people are missing. This is pure terrorism," Kharkiv Mayor Ihor Terekhov wrote on Telegram, translated to English by Google.
More than 30 vehicles also were damaged in the blast in Ukraine's second-largest city.
"This strike on Kharkiv is another manifestation of Russian madness, there is just no other way to put it," Ukrainian President Volodymr Zelensky said in a video message posted on his official Telegram account.
"Only such madmen as Putin are capable of killing and terrorizing people in such a vile way. We already know that there are wounded, and there are killed. My condolences to the families and friends. Anyone who has been affected will get the help they need."
The attack comes just two days after a Russian missile strike on Kharkiv killed at least seven people and wounded over a dozen more.
At least 11 people were killed by Russian missile strikes in Kharkiv last weekend.
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