Bulgarian media have reported that a spokesman for the national football association named the player involved as Yordan Minev, a 32-year-old defender with Ludogorets Razgrad.
FIFA said the player, who it did not identify, failed a doping control after Bulgaria's 2-1 win against Malta in Valletta on September 10.
"The analysis of the A sample has revealed the presence of prohibited substances," FIFA said in a statement.
Minev did not play in Malta, but all squad members can be selected among the two players typically chosen at random to give samples.
FIFA have imposed an initial 30-day suspension from all football, which includes Bulgaria's final two qualifiers against Armenia and the Czech Republic.