They say the An-26 plane was hit at an altitude of 6,500m (21,325ft).
The plane was targeted with "a more powerful missile" than a shoulder-carried missile, "probably fired" from Russia. The crew survived, reports say.
Russia has made no comment. Separately, Nato reported a Russian troop build-up near the Ukraine border.
A Nato official confirmed to the BBC that the alliance had observed a significant increase of Russian troops, bringing their number to up to 12,000.
Russia denies supporting and arming the separatists, and has invited officials from the Organization for Security and Co-operation in Europe (OSCE) to monitor its border with Ukraine.
A statement on Ukraine President Petro Poroshenko's website said the An-26 was taking part in the "anti-terror operation" in the region.
Ukrainian Defence Minister Valeriy Heletei said a search-and-rescue operation was under way to locate missing crew members.
Andriy Lysenko, a spokesman for Ukraine's security and defence council, was later quoted by Ukrainian media as saying that eight people had been on board the plane.
Don't stop now. Go in there and clean house. Kill every last one of the fascist bastards that have been torturing and murdering children, women, and innocent civilians. Spare them no quarter.
Then go to Kiev, take Poroshenko, and give him the same treatment he dished out to those innocents. That guy is the epitome of evil.