The 27-year old made the podium at Rio 2016 in the men's 85kg category with a lift of 390kg.
Having already served a two-year doping ban, he could now face a lifetime ban.
"There is no final decision on sanctions relating to the Rio Olympics yet," the International Weightlifting Federation (IWF) said in a statement.
The IWF has declined to make any further comment until the case is closed, but the officially endorsed World Weightlifting magazine has promoted fourth-placed Denis Ulanov from Kazakhstan to the bronze medal and lists Sincraian as disqualified.
Norwegian three-time Olympic cross-country skiing medallist Therese Johaug has also failed a doping test for the prohibited steroid clostebol.
Her country's ski federation said the substance had been in dcame from a sun lotion given to her by team doctor Fredrik Bendiksen, who has resigned and described the violation as his "personal mistake as a doctor".
Romanian Olympic weightlifting bronze medallist Gabriel Sincraian has tested positive for the banned substance testosterone.