Sumy lies close to the Russian border and has come under increasing attack for weeks.
The strike hit Sumy's city centre two days after US envoy Steve Witkoff met with Russian leader Vladimir Putin and despite US President Donald Trump urging Moscow to end the war.
"Russia hit the city centre with ballistic missiles. Right when there were many people on the street," Ukraine's state emergency service said.
"People were injured right in the middle of the street, in cars, public transport, and in houses," emergency services said as rescue operations were ongoing.
"According to preliminary data, 21 people have been killed."
The interior ministry said 83 people, including seven children, were wounded in the strike.
Ukrainian leader Volodymyr Zelensky called for a "strong response" from Europe and the US.
"Enemy missiles hit an ordinary city street, an ordinary life: houses, educational institutions, cars on the street," he said on social media.
"And this is on a day when people go to church: Palm Sunday, the feast of the Lord's Entry into Jerusalem."
He added: "Only bastards can do this."
- Second deadly attack -
"Talking has never stopped ballistic missiles and bombs," Zelensky said, two days after Witkoff held hours-long talks with Putin in Saint Petersburg.
Local authorities in Sumy published footage of bodies strewn on the street and people running for safety, with cars on fire and wounded civilians on the floor.
The attack came despite Trump publicly voicing anger at Moscow this month for "bombing like crazy" in Ukraine and calling on it to "get moving" on ending the more than three-year-long war.
Russia has relentlessly attacked Ukraine in recent weeks.
In early April, a Russian attack on the central city of Kryvyi Rig killed 18 people, including nine children.
Sumy has been under increasing pressure since Moscow pushed back much of Ukraine's troops from its Kursk region across the border.
The eastern city so far has been spared from the kind of fighting seen further south in the Donetsk region but Kyiv for weeks has warned that Moscow could mount an offensive on Sumy.
Russia in recent weeks has claimed the capture of a village in the Sumy region for the first time since the early days of its 2022 invasion.
Russia launched its invasion partially through the Sumy region and briefly occupied parts of it before being pushed back by Ukrainian forces.
Moscow has not yet commented on the strike.
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