Synehubov, writing on the Telegram messaging app, said the latest of three attacks on the city in a single day damaged dwellings and an educational institution. Two people were being treated in hospital.
Kharkiv Mayor Ihor Terekhov said an apartment building had been hit and there were seven injured. He suggested that number could rise.
Officials in Kharkiv had earlier reported eight killed in missile attacks.
(Reporting by Ron Popeski and Maria Starkova; Editing by Mark Porter and Lisa Shumaker)
