Reuters news agency quotes military spokesman Vladislav Seleznov as saying 49 military personnel were killed.
The plane was carrying troops and military equipment and was about to land at the city’s airport.
A statement from the ministry said that “terrorists” had “cynically and treacherously” fired on the aircraft.
The ministry offered its condolences to the families of those who died.
The incident came less than a week after pro-Russia rebels launched a series of attacks on Ukrainian forces at Luhansk International Airport.
The airport has been under the control of government forces but the rebels hold most of the rest of the city.
‘Russian’ tanks Luhansk is the main city of one of two eastern regions where pro-Russia separatists have declared independence from Kiev.
An “anti-terrorist operation” by Ukraine government forces has left at least 270 people dead over the past two months.
Meanwhile, the US said it was confident that tanks being used by separatists in eastern Ukraine came from Russia.
“Russia will claim these tanks were taken from Ukrainian forces, but no Ukrainian tank units have been operating in that area,” a US state department spokeswoman said.
“We are confident that these tanks came from Russia,” she added.
The appearance of the tanks, filmed in various towns in the Donetsk region, sparked a row between Kiev and Moscow.
Russia has denied allegations that the tanks had entered Ukraine from its territory. (BBC)