STORY: Burning stalls at the central Maisky market and at least one body could be seen on the ground at the market in Donetsk.
The DAN news agency said 155-mm calibre NATO-standard artillery munitions hit parts of the region on Monday.
Ukrainian officials have since said an attack on a nearby residential block in Donetsk was carried out by the Russian military.
President Vladimir Putin has repeatedly said that the main immediate reason for what he casts as a "special military operation" was to protect the Russian-speakers of the Donbas region from persecution and attack by Ukraine.
Kyiv says Russia's claim of persecution of Russian-speakers is a baseless pretext for sending troops into the country.