Footage circulated online by presidential officials showed people falling to the ground or running for cover after a huge explosion in front of them, seconds after some look up to the sky when they hear what sounds like a missile approaching.
President Volodymyr Zelenskiy condemned the attack, saying a market, shops and a pharmacy had been struck in the industrial city close to the battlefield.
"This Russian evil must be defeated as soon as possible," Zelenskiy said on the Telegram messaging app.
"When someone in the world still attempts to deal with anything Russian, it means turning a blind eye to this reality. The audacity of evil. The brazenness of wickedness. Utter inhumanity."
He later told a press conference in Kyiv that he believed it had been a deliberate attack on "a peaceful city".
Kostiantynivka, which had a population of about 70,000 before Russia's invasion 18 months ago, is about 30 km (19 miles) from the devastated city of Bakhmut, where fighting has been heavy for months.
It is about 560 km from Kyiv, where Blinken was meeting Zelenskiy and other Ukrainian leaders on a visit intended to show support for Ukraine against Russia's invasion.
SERIES OF ATTACKS
Wednesday's strike followed a series of Russian attacks on cities in eastern Ukraine in which civilian infrastructure has been hit, including a popular cafe, a hotel and shops.
It also followed air strikes several hours earlier on Kyiv and the southern region of Odesa. No casualties were reported in the capital but local officials said one person was killed in the Odesa region.
Interior Minister Ihor Klymenko said the search and rescue operation in Kostiantynivka had been completed."
"As of 18:00 (1500 GMT) 17 people were killed and 32 were injured as a result of Russian shelling," he said.
Police said the market had been crowded when it was hit at around 2.00 p.m. (1100 GMT), and that nearly 30 shopping kiosks, an apartment block, a bank and cars were damaged.
A video released by police showed rescuers searching through the kiosks and, as bodies were taken out in black sacks, people shouting: "Who have you found?"
The video also showed a pharmacy with its floor covered in blood.
"At the moment of the strike civilians were here, they were buying medicines and this is what happened. People died here, the entire floor is covered in blood," a local police spokeswoman is heard saying in the video.
Russia did not immediately comment on the attack, and has denied deliberately targeting civilians. The Kremlin had earlier on Wednesday said of Blinken's visit that Moscow believed Washington planned to continue funding Ukraine's military "to wage this war to the last Ukrainian".
