The 21-year-old South African, who played for the Blue Bulls before joining Stade Francais in October, failed the random test after his side's 42-25 defeat at Montpellier in the penultimate round of the regular season.
"Without prejudging the rest of the procedure, and pending further investigation and development of the ongoing procedure, Stade Francais has decided to allow Hendre Stassen to take the time to organise his defence and suspend his involvement with the club," said the club in a statement.
"Stade Francais attaches the utmost importance to sports ethics and makes the fight against doping a constant priority.
"The club will co-operate with all relevant bodies and will accept the conclusions of the proceedings."
The suspension marks further trouble for Stassen who is currently the subject of another police investigation in South Africa after he allegedly assaulted 26-year-old dentist Markus Botes outside a Pretoria nightclub during the early hours of June 15.
Botes required corrective surgery prompting the charge to be elevated to the more serious crime of assault with the intent to commit grievous bodily harm.