"The terrorists cynically and treacherously fired with a large-calibre machine gun hitting an Ilyushin-76 of the Ukrainian air force which was carrying troops on rotation and was about to land at Lugansk airport," the ministry said in a statement.
The four-engine jet was also carrying "equipment".
The ministry offered its condolences to the families of the "killed soldiers", but did not give their numbers.
Lugansk, which is close to the Russian border, is the main city of one of two eastern regions hit by pro-Moscow separatist violence and which has declared its independence from Kiev.
An "anti-terrorist" clampdown by Ukrainian armed forces has left at least 270 people dead over the past two months.
The attack came less than a week after the rebels fighting Ukraine's Western-backed government launched serious attacks on Lugansk International Airport.
The assaults, which took place Saturday evening and Sunday morning in the immediate wake of the inauguration of Ukraine's new President Petro Poroshenko, did not result in any injuries among the defenders.
But one of the Ukrainian paratroopers guarding the airport told AFP at the time it was clear the rebels were trying to destroy the building which controls the power supply to the airport.
"It's the first time we have had an attack of this kind. Up till now, we've only had a few skirmishes," he said.
Pro-Russian separatists proclaimed the independence of the "Lugansk People's Republic" in May, at about the same time as the neighbouring "Donetsk People's Republic".
The two districts have been the scene of ceaseless fighting between Ukrainian forces and pro-Russian insurgents that have killed more than 200 people since mid-April.
When approached by AFP, a spokesman for the "Lugansk People's Republic" could not confirm the assaults on the airport, which has been closed for the past month because of the instability in the region.
The airport is one among very few areas in the Lugansk area not controlled by the separatists, who have taken over most of the cities, set up numerous roadblocks and recently seized several checkpoints on the border with Russia.
The international airport at the nearby city of Donetsk briefly came under rebel control late last month.
The Ukrainian authorities took it back in fighting that cost the lives of dozens of fighters, mostly of Russian nationality, according to a report issued by Donetsk insurgents.
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