We derive a microscopic theory of drag for a Bose-Einstein condensate interacting with a moving reservoir. Starting from interactions between a condensate and a drifting fermionic bath, we integrate out the bath degrees of freedom within the Born–Markov approximation to obtain an effective Gross–Pitaevskii equation with a drag potential. From this potential we derive an effective drag force and obtain a closed expression for the drag coefficient, determined by the reservoir density fluctuations and the condensate density profile. As an application, we simulate the drag for an exciton–polariton condensate interacting with a drifting electron gas.