World soccer's ruling body said the chairman of its disciplinary committee made the U-turn "following clarification by medical bodies."
"It appears that there is no circumstantial evidence that anti-doping rules have been violated," FIFA added.
The earlier statement had spoken of "an adverse analytical finding" from the doping control after the September 10 game, which Bulgaria won 2-1, with the player suspended for 30 days.
FIFA did not divulge the player's identity, or name any substance, but Minev confirmed to reporters outside the Bulgarian Football Union headquarters that he was the one involved.
"It's a shock for me, it was like they told me I'm pregnant because I never took even a pill in my career," he said.
"I only had a painkilling injection and the doctor described everything in the documentation before the doping test following the match against Malta. I have not done anything wrong and I hope that I will continue playing."
Bulgaria are second in European Group B with 13 points from eight games, seven behind Italy who have already guaranteed first place and qualified.
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