Self proclaimed governor of Donetsk Vyacheslav Ponomaryov declared a curfew there on Sunday.
"The curfew comes into effect today - from midnight (2100 GMT) to 6am (0300 GMT), during which time it would be forbidden to be in the streets"- he said.
The Ukrainian Interior Ministry said at least three people were killed and three others injured in the shooting incident at a makeshift checkpoint outside Slavyansk on April 20.
The identity of the attackers was not immediately clear.
Russia's Foreign Ministry expressed "outrage" over the incident, saying it proved that Ukrainian authorities do not wish to disarm "nationalists and extremists."
Pro-Russian authorities in the region presented documents and other materials that they alleged showed that the Ukrainian far-right nationalist group Right Sector was responsible.
Right Sector denied any involvement and instead accused Russian special services.
The Ukrainian Security Service said no Ukrainian organization was involved. It denounced the incident as a "provocation" staged by outsiders.