"A report by a drug clinic in the area found that there were illegal substances inside Gia Grigalava's internal system," the club said on their official website (www.fc-anji.ru).
"We will do everything possible in order to find out the truth and will do this as openly as possible," general director Sergei Korablev said.
"Anzhi will take action, which adheres to Russian law, including anti-doping agency RUSADA and football trade unions," Korablev added.
The 25-year-old Grigalava told Championat.com that he was in dispute with the club over his contract.
"The whole problem is because of my contract with Anzhi," Grigalava said.
"I have not agreed to take a pay cut and therefore I was sent down to play with the reserves. Then they thought of things to burden me with. They are probably just tired of chasing me and understood that there is no point.
"Everyone understands that I am being set up. I do not drink and I do not smoke, let alone take anything stronger."
Grigalava, who has played 16 times for Georgia, joined Anzhi in 2013 from fellow Russian side Krylya Sovetov Samara.
Under owner Suleyman Kerimov, the club from the North Caucasus embarked on a multi-million dollar spending spree to bring in high-profile players including former Cameroon striker Samuel Eto'o.
Anzhi were relegated from the Russian Premier League at the end of the 2013-14 season after Kerimov decided to cut costs, leading to all the major signings being sold.
They currently lead the Russian first division.
(Editing by Amlan Chakraborty and Ed Osmond)
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