Varon failed an out-of-competition doping control on Saturday in Leverkusen. Colombia played Sweden in their opener yesterday with Sandra Sepulveda in goal, losing 1-0.
Fifa did not say what substance was involved and the player has the right for her "B" sample to be tested. The last doping case at the men's World Cup was Diego Maradona, who was kicked out of the 1994 event in the United States after testing positive for stimulants. He was banned for 15 months.
Meanwhile, eight players from Mexico's team at the Copa America have been suspended for six months and fined $4,100 for violating team training rules. Reports said the incidents took place in Ecuador during training and involved players having female guests in their rooms.
Mexico are fielding a youth team for the Copa America and the players involved are Israel Jimenez, Nestor Vidrio, Jonathan Dos Santos, Marco Fabian, Jorge Hernandez, Javier Cortes, David Cabrera and Nestor Calderon.
Mexico beat Ecuador 1-0 on Saturday in their final warm-up match and the incidents are said to have taken place after the match.
"I am not going into details," said director of national teams selection Hector Gonzalez Inarritu . "The rules were broken, the code of discipline was broken and I have to act."
The players are likely to be replaced before the tournament gets underway on Friday in La Plata when hosts Argentina play Bolivia.