The explosion on Tuesday night at the Defence Ministry base in the Kurchaloi settlement, about 100km from Chechnya's capital, Grozny, destroyed a two-storey building that housed the unit. Russia's Vostok battalion is stationed at the base.
Military and local emergency ministry officials said on Wednesday that the reason for the blast remained unknown.
A criminal investigation has been launched as rescuers continue to search for more people in the ruins.
Earlier, officials said it was a gas explosion, but no remains of gas containers or explosives have been found.
According to an interior ministry source quoted by RIA-Novosti up to 43 people could have been in the building at the time.
Russian troops in Chechnya are regularly attacked by separatists trying to overthrow Moscow's rule. But there were no immediate reports of any attack in the area.
An unnamed official told Itar-Tass news agency: "This was not a terrorist attack."