Moreni tested positive for the hormone following the 11th stage of the Tour de France on Thursday - the third competitor to fail a dope test.
He had started the 16th stage in 58th place, 1 hour, 34 minutes
and 45 seconds behind race leader Michael Rasmussen.
He finished 41st on after stage, falling another 21 minutes behind Rasmussen.
Urine tests are conducted daily at the Tour on the stage winner, the race leader and other selected riders.
Stage 11, from Marseille to Montpellier in southern France, was won by
sprinter Robert Hunter, a South African with the Barloworld team.
The Tour has faced a tumultuous few days.
The race leader then, and now, was Rasmussen, who provoked controversy and faced jeers from the crowd at the start of Wednesday's stage after he missed two pre-Tour doping tests.
On Tuesday, Astana team leader Alexander Vinokourov failed a test for blood doping.
The Kazakh had won two stages in this year's race and in the fallout of his failed test his entire team withdrew from the race.
The race was already reeling from the withdrawal of T-Mobile rider Patrik Sinkewitz after he failed a pre-Tour drugs test with high levels of testosterone.
That case saw German TV stations ZDF and ARD immediately suspend their coverage of the Tour.
A number of major sponsors including T-Mobile, Milram and a Swiss bicycle manufacturer are now reconsidering their future association with the Tour.
The UCI, the international body which controls cycling, was confident of a drug-free Tour after all riders in this year's race signed an agreement in which they would forfeit a year's salary as well as the mandatory two-year ban if they were found guilty of doping.
Earlier, two small explosive devices went off along the route of the Tour in northern Spain.
Blasts came after riders had already passed through the Navarra region near the border with France.
A person claiming to represent ETA, the Basque separatist group, had earlier made a bomb threat by phone, Spanish media reported.