The announcement comes after a Russian publication quoted the player's father, Dmitri, as saying in June 2017 that Cheryshev had received growth hormone injections when he played at Spanish side Villarreal.
Dmitri Cheryshev has since said his statements have been twisted by reporters, while the player himself insists his conscience is clear.
Without a medical exemption, the use of growth hormones is considered doping and is punishable with a ban of up to four years.
"An investigation has been opened to get more information regarding this case," a spokesman for Spain's anti-doping agency AEPSAD told AFP.
"The investigation is being carried out in cooperation with Russia's anti-doping agency and in permanent contact with the World Anti-Doping Agency which is aware of the affair and will be informed of the conclusions," the spokesman said, adding it was too soon to draw conclusions.
Cheryshev, who scored four goals in five World Cup games for Russia as they reached the quarter finals, had denied any wrongdoing.
"On my side, everything has been honest and I think there will be no problem," he told Russian sports daily Sport-Express.
"I think we'd better leave this case in the hands of medics, who have done everything right," he told Sport Express.
The 27-year-old striker joined Valencia in August on a season-long loan from Villarreal.