Dozens more were wounded, and several residential buildings destroyed.
The city is under Ukrainian control, but it is part of a region that Russia says it annexed last month.
Zaporizhzhia has been hit repeatedly in recent weeks, as Russia hits back at urban areas after suffering defeats in the south and north-east of Ukraine.
Parts of the Zaporizhzhia region, including its nuclear power plant – which is around 52km (30 miles) from the city – have been under Russian control since early in the invasion.
Ukrainian officials initially put the death toll at 17 but later revised it down.
The BBC’s Paul Adams, who was recently in the city, says the buildings struck are not obvious military targets and the attacks seem entirely indiscriminate.
More than 60 civilians are understood to have been killed in and around Zaporizhzhia in the past nine days.
Ukrainian President Zelensky called the shelling “merciless strikes on peaceful people again”.
“Absolute meanness,” he said. “Absolute evil. Savages and terrorists. From the one who gave this order to everyone who fulfilled this order. They will bear responsibility. For sure. Before the law and before people.”
The Ukrainian regional governor in Zaporizhzhia, Oleksandr Starukh, said 12 Russian missiles had partially destroyed a nine-storey building, and levelled five other residential buildings.
“There may be more people under the rubble. A rescue operation is under way at the scene. Eight people have already been rescued,” he said on Telegram.
Survivors of the strikes have spoken of the moment they were woken by the blasts.
Kateryna Ivanova and her family were forced to run to the bathroom as their apartment filled with smoke, she told AFP news agency.
After managing to run into the street, Ms Ivanova said she was met by a neighbour who “screamed that her husband was dead”.
Another resident, 38-year-old Lyudmyla, told Reuters news agency how she rushed to wake her children and move them to safety after a “roaring” blast “completely destroyed” the door to her home.
Her 10-year-old son Bohdan described the missile strike as “horrific” and said he was woken by the sound of screaming.
Meanwhile, a power line supplying the nuclear plant has been reconnected after shelling resulted in a cut on Friday night, the head of the International Atomic Energy Agency (IAEA), Rafael Grossi, said.
“Our team at #Zaporizhzhya confirms the offsite power line lost yday was restored & #ZNPP is reconnected to the grid – a temporary relief in a still untenable situation,” he tweeted on Sunday.
Mr Grossi said he would call on both sides to support a protection zone around the plant. Russia and Ukraine have blamed each other for the shelling.
Meanwhile, Russian divers are beginning a fuller examination of the damage done by Saturday’s explosion on the road and rail bridge linking occupied Crimea with Russia.
Though limited traffic has resumed along one lane, a section of the bridge was brought down by the blast.
Security has been tightened and Russian President Vladimir Putin has ordered a full investigation.