Former Russian anti-doping agency worker Vitaly Stepanov made the claims on CBS network's 60 Minutes programme.
He said he was told of a cover-up by Grigory Rodchenkov, the former head of Moscow's anti-doping laboratory.
Wada president Craig Reedie said the agency will act "immediately".
Rodchenkov was not interviewed by the programme, but Wada will now seek access to journalists' recordings of conversations.
The BBC and Wada have been unable to independently verify the allegations made in the programme, while Russia's sports ministry said it was "certain about transparency of doping control" in Sochi.
Reedie added: "Mr Rodchenkov was of course interviewed by Wada's Independent Commission that exposed widespread doping in Russian athletics last year.
"Yet, regrettably, he was not forthcoming with such information related to the Sochi Games. It is surprising to hear these views so many months after the Commission concluded its work."
Natalia Zhelanova, anti-doping advisor to the Russian Minister of Sport, said: "Russia acknowledges the importance of stamping out doping, and we are doing everything we can to achieve this. We acknowledge there are issues with doping in Russia, just as there are across the world.
"We are cooperating with a wide range of anti-doping organisations in these efforts, including Wada, and have nothing to hide in the fight against doping."
Russia won 13 gold medals at the Sochi Winter Olympics. The names of the alleged drug cheats were not revealed in the CBS programme.
