Local people said a rebel rocket launcher recently seen in the area may have been the target.
The Donetsk city council said four apartment buildings in the southern part of the city were damaged by artillery barrages. Shocked residents gathered around in the morning, and some left flowers on the pavement to commemorate the victims, AP reported on Friday.
"Nina, my godmother, was blown into pieces right in front of the apartment. They only were able to identify her by her dressing gown," said 55-year old Yevgeny Isayev. He pointed at a crater left by a projectile that landed next to the apartment building's entrance.
Another resident, Marina Barsuk, 53 said the shelling came a few days after rebels had positioned a Grad multiple rocket launcher near the apartment building and fired at Ukrainian positions. She and other residents believed the shelling came from the Ukrainian side in retribution.
Such exchanges of artillery and rocket barrage have raised the death toll among civilians as the Ukrainian forces have closed in on the main rebel bastion.
In an ominous signal that fighting will likely to escalate further, a top rebel leader, Alexander Zakharchenko, boasted Thursday about seizing 18 Grad systems from the Ukrainian military.
Government forces and the rebels use the same Soviet-made Grad (Hail) launchers, which fire unguided rockets at a distance of up to 20 kilometers (12 miles). Their accuracy is very poor, making collateral damage from shelling populated areas inevitable.
Ukrainian officials have adamantly denied that government forces were shelling populated areas, but witness testimony has pointed to the contrary.
Explosions were also heard elsewhere in Donetsk overnight, but there was no immediate word about casualties there.
Ukrainian troops routed the pro-Russian insurgents from smaller towns in the region earlier this month and have now encircled Donetsk, where fighting has crept closer to the city center. The city council said it was working to keep transport services running and to repair gas networks in apartment buildings. An estimated 300,000 of the city's 1 million residents have fled.
The insurgency in mostly Russian-speaking in eastern Ukraine flared up in April following Moscow's annexation of Crimea in response to the ouster of Ukraine's former pro-Russian president. Ukraine and Western countries have accused Moscow of backing the mutiny with weapons and soldiers. The West also accused Russia of most likely providing the insurgents with surface-to-air missiles that may have been used to shoot down a Malaysia Airlines passenger jet over rebel-held territory on July 17, killing all 298 people on board.
The Russian government has repeatedly denied all those charges.