A resident looks for belongings in an apartment building destroyed during fighting between Ukrainian and Russian forces in Borodyanka, Ukraine, Tuesday, April 5, 2022. AP
"So far we know about 8 dead... The number of injured has increased to 13 people," the ministry said on social media.
The strikes hit around 10:00 am (0700 GMT) at two intersections that were busy with pedestrians, witnesses told AFP.
A residential building, an annex to a printing house and three cars were set on fire in the attack, the ministry said.
AFP journalists arriving on the scene in the afternoon saw three charred vehicles in front of an automobile supply store.
Traces of blood were visible at both intersections.
"There were explosions everywhere, I didn't know where to hide," Nadya Bereinaya, 69, told AFP. "Today is Saturday, so there was a lot of people."
Pavlo Kyrylenko, governor of the Donetsk region where Lyman is located, said "at around 10:00 am, the Russians struck the town with multiple rocket launchers".
Lyman, a major rail hub, was initially captured by Russian forces but then re-taken by Ukraine's army in October.
Ukraine has reported Russian offensive operations in the area this week.
In the Russian-controlled town of Oleshky in southern Ukraine, an emergency services official was quoted by TASS news agency as saying two civilians were killed by Ukrainian fire overnight.
Ukrainian forces last month began a counteroffensive to take back Russian-controlled territory in the east and south of the country.
Facing powerful Russian defensive lines, they have only recaptured a few hundred square kilometres and around a dozen villages after more than a month.