"Today, at about 5 p.m. Moscow time, when performing a scheduled training flight near the village of Dolzhanskaya of the Krasnodar Territory, an L-39 jet trainer crashed and fell into the water," the ministry said.
It said a search and rescue team was looking for pilots in the area of the crash.
"The plane was flying without ammunition. According to preliminary information, a technical malfunction could have caused the crash," the ministry said.
Earlier this month, a helicopter crashed in Russia's Kostroma region, killing three people.