Yuri Biryukov, an adviser to President Petro Poroshenko, said on his Facebook page that the rebels had also injured nine soldiers in the attack. In a statement published online, the Donetsk City Council said more than a dozen buildings in the north of the city were damaged by the shelling.
"The situation in the city is very tense" and artillery was heard throughout the night, the statement said.
The rebels hold key points inside the city itself, an industrial hub with a pre-war population of about one million. Ukrainian security forces and the pro-Moscow separatists have clashed repeatedly in recent weeks, with residential areas caught up in fighting centered on the government-held airport.
The ongoing violence is threatening to imperil the shaky ceasefire. Ukrainian President Petro Poroshenko has been at pains to insist that his peace plan is working to a skeptical audience at home.
According to a UN human rights official, more than 3,500 people have been killed in the fighting and almost 350,000 others forced to flee their homes.