The November elections to select a new leader were announced after his assassination.
The Ukrainian Foreign Ministry said earlier this month that neither Kyiv nor the international community will recognize the elections on the "temporarily occupied territories" in eastern Ukraine.
The United States and the European Union have also condemned plans by Russia-backed separatists to hold "elections," calling them "phony procedures" that undermine peace efforts in the region.
Russia's actions in eastern Ukraine and its seizure and annexation of Ukraine’s Crimea Peninsula led the United States and the EU to impose sanctions against Moscow and has heightened tensions between Russia and the West.
Gennady Filonenko, a Communist Party member, told reporters that about 50 people were inside the building during the explosion.
"A package was found at the site of the explosion. Two women were injured, one of them sustained severe burns," he said.
Communist Party leader Boris Litvinov said the building was heavily damaged.
The incident is the latest violence in eastern Ukraine where the Moscow-backed separatists have been fighting the central government in Kyiv since 2014 in a war that has killed more than 10,300.
It comes about a month after Donetsk separatist leader Aleksandr Zakharchenko was assassinated by a bomb blast in a cafe in the eastern Ukrainian city.
At least four people, including a candidate for the head of the Russia-backed formation called the Donetsk People's Republic (DPR) have been injured in an explosion in Donetsk.
The explosion on September 29 took place in a building where the local Communist Party held a meeting, officials in Ukraine's separatist regions said.
Igor Khakimzyanov, a candidate for the post of heading the DPR who was nominated by the Communist Party, said he was entering the building when the explosion happened.
"We were entering the building with one of my campaign staff. An explosion thundered as we were entering [the building],” he told reporters.
Separatist Telegram channels posted pictures online that appeared to show his injuries.