The attack struck the Saltivskyi district at about 4am, destroying apartments on the lower floors. Emergency crews rescued 32 people from the building and searched the damaged floors for anyone still trapped inside.
The injured children were aged between three and 15. Two boys, aged eight and 12, were taken to hospital, while the others received treatment at the scene. Several victims were also treated for injuries and acute stress reactions.
Rescue workers, police and medical teams continued clearing debris on Monday. Authorities said investigators were trying to determine which weapon had been used.
The strike came during a wider wave of Russian overnight attacks. Four people were injured in Kyiv, while preliminary reports indicated that two others were hurt in Odesa.
The attack is the latest to hit Kharkiv, a major city in north-eastern Ukraine that has faced repeated Russian strikes since the full-scale invasion began.