The mortar blasts damaged three apartment blocks and five houses in the Budyonivsky district in the southeast of the million-strong industrial city, the city council said in a statement.
Shelling also destroyed two houses in a village on the western outskirts of the mining hub but no casualties were reported, the statement said.
An AFP journalist reported that heavy shelling could be heard again mid-morning today from central Donetsk.
The latest deaths come as Ukraine's military says it is gearing up to retake the main insurgent bastion in the east, after a month of solid advances saw government forces encircle insurgents hunkered there.
Civilians have been hit hardest, with more than 285,000 fleeing their homes over, according to the UN refugee agency UNHCR, which warned of "a massive exodus" if fighting intensifies.
Across the region, local authorities in the second largest rebel bastion of Lugansk have warned of a looming "humanitarian catastrophe" as water, food and fuel supplies have dried up.
Ukraine's military meanwhile reported shelling overnight of four of its positions across the east, but no casualties.
Yesterday Ukrainian forces said that they had lost 18 soldiers in clashes with rebels over the preceding 24 hours, the highest daily death toll in weeks.
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