The final fate of massive stars depends on many factors. Theory suggests that some with initial masses greater than 25 to 30 solar masses end up as Wolf-Rayet stars, which are deficient in hydrogen in their outer layers because of mass loss through strong stellar winds. The most massive of these stars have cores which may form a black hole and theory predicts that the resulting explosion of some of them produces ejecta of low kinetic energy, a faint optical luminosity and a small mass fraction of radioactive nickel. An alternative origin for low-energy supernovae is the collapse of the oxygen-neon core of a star of 7-9 solar masses. No weak, hydrogen-deficient, core-collapse supernovae have hitherto been seen. Here we report that SN 2008ha is a faint hydrogen-poor supernova. We propose that other similar events have been observed but have been misclassified as peculiar thermonuclear supernovae (sometimes labelled SN 2002cx-like events). This discovery could link these faint supernovae to some long-duration gamma-ray bursts, because extremely faint, hydrogen-stripped core-collapse supernovae have been proposed to produce such long gamma-ray bursts, the afterglows of which do not show evidence of associated supernovae.