The missile struck a residential area near a children's playground and wounded more than two dozen others, according to the head of the city's military administration.
Unverified videos on social media appeared to show bodies lying on a street, while another showed a plume of smoke rising into the evening sky.
"Sixteen lives lost. Six of them children. There are no words. This is the kind of pain you wouldn't wish on your worst enemy," regional governor Sergiy Lysak said on Telegram.
US President Donald Trump has been pushing for a speedy end to the more than three-year war since taking office, but his administration has failed to broker a ceasefire despite talks with both sides.
Zelensky said the attack showed Russia had no interest in stopping its invasion.
"There is only one reason why this continues -- Russia does not want a ceasefire and we see it. The whole world sees it," he said.
The Ukrainian leader was born in Kryvyi Rig, an industrial city which had a pre-war population of around 600,000 people.
Russian President Vladimir Putin rejected a joint US-Ukrainian proposal for an unconditional and full ceasefire in March, while the Kremlin has made a US-proposed truce in the Black Sea dependent on the West lifting certain sanctions.
US Secretary of State Marco Rubio said earlier on Friday that Trump was not "going to fall into the trap of endless negotiations" with Russia over the invasion.
"We will know soon enough, in a matter of weeks, not months, whether Russia is serious about peace or not," he said.
- 'War crime' -
Kryvyi Rig, in Ukraine's central Dnipropetrovsk region, is about 60 kilometres (37 miles) from the front line, and has regularly been targeted by Russian drones and missiles.
A previous Russian ballistic attack on the city on Wednesday killed at least four people and wounded more than a dozen others.
Oleksandr Vilkul, the head of the city's military administration, said the missile landed near a children's playground.
Five apartment buildings were damaged, interior minister Igor Klymenko said.
He said police had blocked off the area to maintain order.
"The police are documenting the consequences of Russia's war crime and accepting statements from the victims," Klymenko added.
Social media video from the scene showed a car in flames, while people could be heard shouting.
Andriy Kovalenko, a Ukrainian official tasked with countering disinformation, described the missile involved in the attack as an "Iskander".
The Iskander is a Russian ballistic missile system that can have a range of up to 500 kilometres (311 miles).
"This is a deliberate strike to kill a large number of people," Kovalenko said.
Zelensky accused Russia of regarding diplomacy as an "empty word" in his evening address.
"A ceasefire could have been reached by now and it is Putin who rejects it," he said.
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