A large number of faint galaxies, born less than a billion years after the Big Bang, have recently been discovered. Fluctuations in the distribution of these galaxies contributed to a scatter in the ionization fraction of cosmic hydrogen on scales of tens of megaparsecs, as observed along the lines of sight to the earliest known quasars. Theoretical simulations predict that the formation of dwarf galaxies should have been suppressed after cosmic hydrogen was reionized, leading to a drop in the cosmic star-formation rate. Here we report evidence for this suppression. We show that the post-reionization galaxies that produced most of the ionizing radiation at a redshift z approximately 5.5 must have had a mass in excess of approximately 10(10.9 +/- 0.5) solar masses (M(o)) or else the aforementioned scatter would have been smaller than observed. This limiting mass is two orders of magnitude larger than the galaxy mass that is thought to have dominated the reionization of cosmic hydrogen (approximately 10(8) M(o)). We predict that future surveys with space-based infrared telescopes will detect a population of smaller galaxies that reionized the Universe at an earlier time, before the epoch of dwarf galaxy suppression.