An Associated Press reporter on the scene saw gaping holes in the side of apartment block after it was fired on.
Around 50 people took refuge in a nearby underground car park and the area was heavy with the smell of household gas.
Although Donetsk is the main stronghold of rebel commanders, the government has refrained to date from attacks on the center of the city.
Rebels accuse the government of using heavy artillery against residential neighborhoods. Ukraine's government says it has banned the use of artillery in residential areas and in turn says separatists target civilians to discredit the army.