The population of artificial satellites and space debris orbiting the Earth imposes non-negligible constraints on both space operations and ground-based optical and radio astronomy. The ongoing deployment of several satellite ‘mega-constellations’ in the 2020s represents an additional threat that raises significant concerns. The expected severity of its unwanted consequences is still under study, including radio interference and information loss by satellite streaks appearing in science images. In this Letter, we report a new skyglow effect produced by space objects: increased night sky brightness caused by sunlight reflected and scattered by that large set of orbiting bodies whose direct radiance is a diffuse component when observed with the naked eye or with low angular resolution photometric instruments. According to our preliminary estimates, the zenith luminance of this additional light pollution source may have already reached ∼20 μcd m−2, which amounts to an approximately 10 percent increase over the brightness of the night sky determined by natural sources of light. This is the critical limit adopted in 1979 by the International Astronomical Union for the light pollution level not to be exceeded at the sites of astronomical observatories.