The police chief of the war-torn region of Donetsk said the long-range Grad rockets hit a market in an eastern district facing roads that have come under attack from separatist militias in recent days.
The southeastern Sea of Azov city of nearly 500,000 sits on a highway connecting guerrilla-held regions to the east and the Black Sea peninsula of Crimea that Russia annexed from Ukraine in March.
A massive rebel assault on the port in August led to intense fighting that saw Kiev repel the attack at a heavy cost that soon prompted Ukrainian President Petro Poroshenko to agree to a September 5 truce.
The separatist leader of Donetsk vowed yesterday to escalate the nine-month campaign and seize lands in southeastern Ukraine that are currently under control of the pro-Western authorities.
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The pro-Kiev volunteer Azov regiment based around the city said there were "many wounded" in the attack. The Mariupol administration said the rockets hit a large market in one of the city's main residential districts.
"Right now, there are problems with the cell phone network so it is impossible to call relatives who live in that part of town," Mariupol resident Eduard told AFP by telephone.
There was no immediate comment on the battle from rebel leaders.