The regional governor Oleh Syniehubov says a further 16 people have been taken to hospital with injuries.
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Six postal workers have been killed and a further 16 injured after a missile hit a distribution centre in eastern Ukraine late on Saturday night.
Ukrainian President Volodymyr Zelensky said on Telegram the Nova Poshta sorting office was struck in Kharkiv.
Pictures from the scene posted on President Zelensky’s account showed the building with windows blown out.
Kharkiv’s regional governor Oleh Syniehubov said the victims all worked for the postal company.
Police said 22 people were inside when the suspected S-300 rocket hit the building just before 22:30 local time (20:30 BST).
Investigators, together with criminologists and forensic experts, are conducting an examination of the bodies of the dead, police added on social media.
Writing on Telegram himself, Mr Syniehubov said the victims were aged between 19 and 42, with some suffering shrapnel wounds from the blast.
He said the private delivery company in the western Kharkiv suburb of Korotych was “strictly a civilian site”.
“The Russians have inflicted more terror on Kharkiv’s peaceful population,” he added.
Image source, Reuters
President Zelensky said a rescue operation was continuing, with emergency services working at the scene.
Russia has not yet commented on the alleged strike, but has previously denied targeting civilians during its invasion of Ukraine.
Mr Syniehubov said seven people were in hospital in a “moderate condition” and seven men were in a “serious condition”.
Kharkiv, which is Ukraine’s second largest city, is located only 30km (19 miles) from the Russian border.
Image source, Reuters
The north-eastern city was heavily bombed during the first weeks of the war in February 2022.
Earlier this month, Kharkiv Mayor Ihor Terekhov said Ukraine’s first underground school would be built in the city to allow children to continue in-person education safely.
Meanwhile in the south, Ukraine has been waging a counter-offensive campaign since June.
The war-torn country aims to sever Russia’s land corridor to the Crimean peninsula – which Russia illegally annexed in 2014.
But the counter-offensive has so far proven slow, bringing only limited territorial gains.