Feedback from massive stars plays a critical part in the evolution of the Universe by driving powerful outflows from galaxies that enrich the intergalactic medium and regulate star formation1. An important source of outflows may be the most numerous galaxies in the Universe: dwarf galaxies. With small gravitational potential wells, these galaxies easily lose their star-forming material in the presence of intense stellar feedback1,2. Here, we show that a nearby dwarf galaxy—the Small Magellanic Cloud—has atomic hydrogen outflows extending at least 2 kiloparsecs from the star-forming bar of the galaxy. The outflows are cold (< 400 K) and may have formed during a period of active star formation 25-60 Myr ago3,4. The total mass of atomic gas in the outflow is about 107 solar masses (that is, about 3 per cent of the total atomic gas of the galaxy). The inferred mass flux in atomic gas alone, M˙ H I ≈ 0.2-1.0 solar masses per year, is up to one order of magnitude greater than the star-formation rate. We suggest that most of the observed outflow will be stripped from the Small Magellanic Cloud through its interaction with its companion, the Large Magellanic Cloud, and the Milky Way, feeding the Magellanic Stream of hydrogen encircling the Milky Way.