In recent years, certain luminous extragalactic optical transients have been observed to last only a few days. Their short observed duration implies a different powering mechanism from the most common luminous extragalactic transients (supernovae), whose timescale is weeks. Some short-duration transients, most notably AT2018cow, show blue optical colours and bright radio and X-ray emission. Several AT2018cow-like transients have shown hints of a long-lived embedded energy source, such as X-ray variability, prolonged ultraviolet emission, a tentative X-ray quasiperiodic oscillation and large energies coupled to fast (but subrelativistic) radio-emitting ejecta. Here we report observations of minutes-duration optical flares in the aftermath of an AT2018cow-like transient, AT2022tsd (the ‘Tasmanian Devil’). The flares occur over a period of months, are highly energetic and are probably nonthermal, implying that they arise from a near-relativistic outflow or jet. Our observations confirm that, in some AT2018cow-like transients, the embedded energy source is a compact object, either a magnetar or an accreting black hole.