Playmaker Dzagoev went down midway through the first half of Russia's tournament opener against Saudi Arabia on Thursday.
"Alan Dzagoev damaged the muscles in the back of the thigh," the hosts said in a brief statement.
"The terms of treatment will be determined by the results of the upcoming MRI [scan]."
Despite Dzagoev's injury, Russia would go on to secure a 5-0 victory over Saudi Arabia in the tournament opener.