Czech Tennis Association president Ivo Kaderka said the sample was taken after the Davis Cup quarterfinal against Argentine on July 10-12.
Kaderka said Minar was taking an unspecified food supplement that apparently contained a derivative of the banned stimulant pseudoephedrine.
The ITF in London said it had no comment.
The 25-year-old Minar, who is ranked 66th, denied deliberate doping.
"I have never consciously taken a banned substance," he said in a statement sent to the CTK news agency. "This is why I rejected the accusation of doping in my reaction sent to the ITF."
Minar cited an injury when he pulled out of the upcoming U.S. Open on Friday.
Kaderka said he interpreted Minar's decision to withdraw as an "offer to deal with the matter in a professional way," not an admission of guilt.
It's unclear whether Minar will be able to play in the Davis Cup semifinal against Croatia on Sept. 18-20.
Minar, who turned pro in 2002 and has never won a tour singles title, won a doubles tournament in Munich this year with Tomas Berdych.
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