Extending quantum communication to space environments would enable us to perform fundamental experiments on quantum physics as well as applications of quantum information at planetary and interplanetary scales. Here, we report on the first experimental study of the conditions for the implementation of the single-photon exchange between a satellite and an Earth-based station. We built an experiment that mimics a single photon source on a satellite, exploiting the telescope at the Matera Laser Ranging Observatory of the Italian Space Agency to detect the transmitted photons. Weak laser pulses, emitted by the ground-based station, are directed toward a satellite equipped with cube-corner retroreflectors. These reflect a small portion of the pulse, with an average of less-than-one photon per pulse directed to our receiver, as required for faint-pulse quantum communication. We were able to detect returns from satellite Ajisai, a low-Earth orbit geodetic satellite, whose orbit has a perigee height of 1485 km.