The 35-year-old, who drives a Lamborghini in the FIA GT1 sportscar world championship, said on his Facebook page that he was "in shock" after the positive test at a race in Spain last month.
He explained that he had long-term health problems and recently asked the governing International Automobile Federation (FIA) for an exemption to allow him to take certain medicines.
"Now I will consult with experts as to how this situation could occur," he said.
The Paris-based FIA, a signatory to the World Anti-Doping Agency (WADA) code, confirmed he had been suspended but could not comment on details of the case.
Enge was stripped of the F3000 title, at the time the feeder series for Formula One, in 2002 after testing positive for cannabis.
The former McLaren and Jordan test driver had already become the first Czech to race in Formula One after starting three grands prix with the now-defunct Prost team in 2001 as a stand-in for injured Brazilian Luciano Burti.
No Formula One driver has ever failed a dope test.