A serviceman armed with an automatic rifle fired shots at a military field camp in the Kostroma region on the Volga, killing the three, the Investigative Committee in charge of major crimes said in a statement.
He also wounded two other servicemen and then committed suicide, investigators said.
Citing preliminary information, the defence ministry said there was a personal motive behind the attacks.
The Investigative Committee, which reports directly to President Vladimir Putin, gave few details, saying only that it had opened a probe into multiple murder.
Since coming to power in 2000, Russian President Vladimir Putin has sought to boost the armed forces, which received new aircraft, tanks and missiles after years of post-Soviet neglect.
But hazing in the army remains a major problem and sometimes leads to suicides or murders. Rights campaigners accuse the military top brass of seeking to cover up instances of bullying.
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