Some people are still believed to be trapped under the rubble as rescuers and bystanders clear the debris.
"Two people died and 22 were injured, including a child. A restaurant and several houses were damaged," Igor Klymenko said on Telegram.
Kramatorsk, once a city of 150,000 inhabitants, is the last major city under Ukrainian control in the east of the country.
It lies about 30 kilometres from the frontline.
