The attack set fire to a two-storey industrial building, a two-storey apartment block and a single-storey house in the city's Osnovyansky district, Oleh Syniehubov, head of the Kharkiv regional military administration, said on Telegram.
Syniehubov said the injured were two women aged 32 and 65, a 56-year-old man and a four-year-old boy. Three of them required hospital treatment.
Kharkiv mayor Ihor Terekhov also reported a drone strike on a residential building and said people may be trapped inside the apartment block.
Ukraine's air force warned of a ballistic missile threat from Bryansk toward Kyiv, later lifting the alert. It said attacks with jet-powered drones and guided aerial bombs continued toward the Kharkiv and Dnipropetrovsk regions, as well as Kyiv and the surrounding region.
Ukrainian rescue services reported five people injured in the strike on the Osnovyansky district, including the four-year-old child.
The accounts differ on the number of casualties: Syniehubov reported four wounded, while the rescue services reported five. The details of the injuries otherwise match.