Russia allegedly targeted the city of Kostiantynivka, killing and wounding many, Ukrainian officials say.
The number of dead in Wednesday’s attack was feared to rise.
The assault came as US Secretary of State Anthony Blinken visited Ukraine’s capital, where he is expected to announce more than $1bn in new funding in a display of Washington’s unflagging support for Kyiv’s fight.
President Volodymyr Zelenskyy condemned the attack, saying a market, shops and a pharmacy had been struck in the industrial city close to the battlefield, and about 30 kilometres (19 miles) from the city of Bakhmut, where fighting has been heavy for months.
Ukrainian officials posted a video on the Telegram messaging app that showed a loud explosion ripping through shopping alleys, with people falling to the ground and some running for cover. Local media described it as a missile attack.
“This Russian evil must be defeated as soon as possible,” Zelenskyy said.
Interior Minister Ihor Klimenko said that in addition to the 16 killed, at least 28 people were wounded in the attack and said it was on the central city market.
Emergency service workers extinguished the fire that damaged about 30 pavilions at the outdoor market, he said.
Klimenko posted pictures on Telegram showing rescue workers sifting through the rubble and carrying out bodies in black sacks.