The drag-free technique is used to force a proof mass to follow a geodesic motion. The mass is protected from perturbations by a cage, and the motion of the latter is actively controlled to follow the motion of the proof mass. We present a theoretical analysis of the effects of quantum fluctuations for this technique. We show that a perfect drag-free operation is in principle possible at the quantum level, in spite of the back-action exerted on the mass by the position sensor.