The "Islamic State" (IS) claimed responsibility for the attack on a concert venue, Crocus City Hall, near Moscow.
IS fighters "attacked a large gathering... on the outskirts of the Russian capital Moscow," the group said in a statement on the Telegram messaging app.
The statement said the attackers had "retreated to their bases safely."
Meanwhile, Russian state news agency RIA Novosti reported that the terrorists allegedly left the concert hall in a white Renault car.
Two weeks ago, the US Embassy in Russia warned that "extremists" had imminent plans for an attack in Moscow.
The embassy had issued its warning several hours after the FSB said it had foiled an attack on a Moscow synagogue by a cell of the militant group "Islamic State."