Kepler's observation of comet tails initiated the research on the radiation pressure of celestial objects and 250 years later they found new incarnation after the Maxwell's equations were formulated to describe a plethora of light-matter coupling phenomena. Further, quantum mechanics gave birth to the photon drag effect. Here, we develop a microscopic theory of this effect which can occur in a general system containing Bose-Einstein-condensed particles, which possess an internal structure of quantum states. By analyzing the response of the system to an external electromagnetic field we find that such a drag results in a flux of particles constituting both the condensate and the excited states. We show that in the presence of the condensed phase, the response of the system acquires steplike behavior as a function of the electromagnetic field frequency with the elementary step determined by the internal energy structure of the particles.