A sample taken after the Davis Cup quarterfinal against Argentine on July 11 contained the banned stimulant methylhexanamine, the International Tennis Federation said.
The 25-year-old Minar claimed he had taken a food supplement that contained the substance.
The ITF said the ban will end on March 10, 2010, and ruled that Minar's results this year from tournaments in Stuttgart, Hamburg and Gstaad should be disqualified.
"The ITF accepted Mr. Minar's account of the background to his positive test," the federation said in a statement. "Under the Tennis Anti-Doping Program, however, it is a player's strict personal duty to ensure that no prohibited substance enters his or her body, whether as an ingredient in a nutritional supplement or otherwise."