"Kuzenkova is facing possible sanctions from the IAAF after a prohibited substance was found in her A sample," the agency said on its website without giving any more details.
The 42-year-old, who has denied any wrongdoing, retired shortly after failing to qualify for the 2008 Beijing Olympics.
Kuzenkova, who was also world champion in 2005, is the latest Russian athlete to face sanctions for a breach of anti-doping regulations.
Earlier on Friday, European under-23 race-walking champion Tatyana Mineyeva was banned for two years after failing a drugs test.
Last week, 2012 Olympic discus silver medallist Darya Pishchalnikova and Russian hammer champion Kirill Ikonnikov, who finished fifth at the London Games, were temporarily suspended by the IAAF for failing drugs tests.
Also last week, the International Olympic Committee stripped shot putter Svetlana Krivelyova of her bronze medal from the 2004 Athens Games.
Krivelyova, 43, who has long since retired from the sport, tested positive for anabolic steroids after her samples from eight years ago were re-tested.