Quiescent galaxies with little or no ongoing star formation dominate the population of galaxies with masses above 2 x 10(10) times that of the Sun; the number of quiescent galaxies has increased by a factor of about 25 over the past ten billion years (refs 1-4). Once star formation has been shut down, perhaps during the quasar phase of rapid accretion onto a supermassive black hole(5-7), an unknown mechanism must remove or heat the gas that is subsequently accreted from either stellar mass loss(8) or mergers and that would otherwise cool to form stars(9,10). Energy output from a black hole accreting at a low rate has been proposed(11-13), but observational evidence for this in the form of expanding hot gas shells is indirect and limited to radio galaxies at the centres of clusters(14,15), which are too rare to explain the vast majority of the quiescent population(16). Here we report bisymmetric emission features co-aligned with strong ionized-gas velocity gradients from which we infer the presence of centrally driven winds in typical quiescent galaxies that host low-luminosity active nuclei. These galaxies are surprisingly common, accounting for as much as ten per cent of the quiescent population with masses around 2 x 10(10) times that of the Sun. In a prototypical example, we calculate that the energy input from the galaxy's low-level active supermassive black hole is capable of driving the observed wind, which contains sufficient mechanical energy to heat ambient, cooler gas (also detected) and thereby suppress star formation.