The 33-year-old, who was due to compete in the women's 3000m steeplechase on Monday, tested positive a few days after her arrival in Brazil on July 26 and has been suspended pending the result of the test on her B sample, sources said.
Danekova, who raced the steeplechase at the 2012 London Olympics but did not get beyond the heats, used the banned blood booster erythropoietin (EPO).
Neither Danekova or her coach Rumen Angelov were immediately available for comment. The athletics programme begins on Friday.
"Unfortunately, we have a positive test," Bulgarian Olympic Committee's Secretary General Belcho Goranov told local media, refusing to name the athlete.
"We await the opening of the B sample test."
Sebastian Coe, president of the International Association of Athletics Federations, addressed the issue of doping on Wednesday, saying: "The last year has sorely tested all of us and all of our fans out there and our responsibility is to shape the future.
"So I genuinely hope that what they feel they're watching is our competitors doing it cleanly, and the vast majority are."
Bulgarian athletics has been marred by a series of doping offences recently. Sprinters Tezdzhan Naimova and Inna Eftimova, middle-distance runners Daniela Yordanova, Vanya Stambolova and Teodora Kolarova, high jumper Venelina Veneva and hammer thrower Andrian Andreev have all tested positive in the last decade.
The country's weightlifting team were banned from Rio for repeated doping offences.
(Additional reporting by Angel Krasimirov; Editing by Bill Rigby and Frank Pingue)
