An 11-month-old baby was among the injured, according to regional governor Oleh Synehubov.
Multiple apartment buildings and cars were damaged, according to media reports.
The Ukrainian foreign ministry said: "In the morning, Russia launched two missile strikes on Kharkiv's civilian infrastructure. Residential buildings in the city center were destroyed. They killed a boy and injured at least 25 people. The search and rescue operations are ongoing."
'Another targeted Russian strike on civilians'
Ukrainian Interior Minister Ihor Klymenko denounced the attack as "another targeted Russian strike on civilians."
On Thursday, at least 51 people, including a six-year-old boy, were killed in a Russian attack on a village in the Kharkiv region, according to Ukrainian officials.
On Friday, the death toll from the attack rose to 52, Ukrainian state news agency Ukrinform reported.
Russia attacks Ukrainian port
In a separate attack in the early hours of Friday, Russian drones damaged a grain silo in the Izmail district of Ukraine's southern Odesa region, the Reuters news agency reported.
Nine trucks caught fire at the site, but the fire was put out quickly, regional governor Oleh Kiper said.
"The enemy once again targeted the border and port infrastructure of the Izmail district," he added, as quoted by Reuters.
Ukraine said its air defences shot down 25 of 33 drones launched by Russia early on Friday from the annexed Crimea peninsula.
The drone strikes targeted the Odesa and Mykolaiv regions in the south, Dnipropetrovsk in the southeast, Cherkasy and Zhytomyr in the centre, and the Kharkiv region in the northeast, the Ukrainian air force said on the Telegram messaging app, according to Reuters.
Russia invaded Ukraine on February 24, 2022, launching the largest military campaign in Europe since World War II.
Friday is day 590 of Russia’s war on Ukraine.
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Source: Reuters, ukrinform.net, IAR, PAP