It said two men from an unnamed former Soviet republic fired on volunteer soldiers during target practice and were killed by return fire.
The ministry called the incident a terrorist attack.
The shooting comes amid a hasty mobilisation ordered by President Vladimir Putin to beef up Russian forces in Ukraine — a move that triggered protests and caused hundreds of thousands to flee Russia.
Putin said Friday that over 220,000 reservists already had been called up as part of an effort to recruit 300,000.
He promised the mobilisation would be wrapped up in two weeks.
The mobilisation was troubled from the start, with authorities issuing confusing signals about who should be called up for service in a country where almost all men under age 65 are listed as reservists.
Even though the Russian leader declared that only people who had recently served in the military would be subject to the call-up, activists and rights groups reported military conscription offices rounding up people without any army experience — some of whom were also unfit for service for medical reasons.
Some of the freshly called-up reservists posted videos of themselves being forced to sleep on the floor or even outside and given rusty weapons before being sent to the front lines.
Russian media reports said some of those who were mobilised were sent to combat without receiving proper training and were quickly killed.
Authorities have acknowledged the mobilisation was often poorly organised and promised to improve the situation.