Kraft was the first ever German woman to win the famed triathlon, considered one of the hardest endurance events in the world when she lifted the trophy in Hawaii on Oct. 17.
However the 35-year-old could be forced to hand back her medal, and faces a ban from competition if a second B sample also tests positive.
According to the newspaper Kraft has already admitted her guilt, and told the organiser of the Ironman in Germay, Kurt Denk, that she had done "something stupid."
The German Triathlon Union (DTU) meanwhile have not named Kraft, and are waiting on the results of her B sample.
The DTU released a statement simply confirming that one of their athletes had tested positive for a banned substance.
"There is a positive test from an athlete," said the DTU in the statement. "If the second B sample tests positive we will make the news public."
EPO has seen widespread use in endurance events, most notably in professional cycling.
A hormone which is already produced by the body, the synthetic version of EPO enhances endurance by boosting oxygen-rich red blood cells which then allow muscles to work for longer and to recover more quickly.