"At 2:51 am, Kharkiv came under aerial attack", Igor Terekhov said on Telegram, adding that "two houses were destroyed and about 20 houses sustained varying degrees of damage".
He added that responders were clearing the rubble and four people had been confirmed dead.
Kharkiv lies around 30 kilometres (18 miles) from the Russian border and has been pounded by Russian aerial attacks throughout the two-and-a-half-year war.
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A Russian strike on Monday damaged the Derzhprom building, a distinctive early Soviet-era modernist skyscraper that has become a symbol of the heavily attacked northeastern city.
The attack injured at least six people and also damaged a medical institution.
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