Magnetars are neutron stars with extremely strong magnetic fields (1013 to 1015 gauss)1,2, which episodically emit X-ray bursts approximately 100 milliseconds long and with energies of 1040 to 1041 erg. Occasionally, they also produce extremely bright and energetic giant flares, which begin with a short (roughly 0.2 seconds), intense flash, followed by fainter, longer-lasting emission that is modulated by the spin period of the magnetar3,4 (typically 2 to 12 seconds). Over the past 40 years, only three such flares have been observed in our local group of galaxies3-6, and in all cases the extreme intensity of the flares caused the detectors to saturate. It has been proposed that extragalactic giant flares are probably a subset7-11 of short γ-ray bursts, given that the sensitivity of current instrumentation prevents us from detecting the pulsating tail, whereas the initial bright flash is readily observable out to distances of around 10 to 20 million parsecs. Here we report X-ray and γ-ray observations of the γ-ray burst GRB 200415A, which has a rapid onset, very fast time variability, flat spectra and substantial sub-millisecond spectral evolution. These attributes match well with those expected for a giant flare from an extragalactic magnetar12, given that GRB 200415A is directionally associated13 with the galaxy NGC 253 (roughly 3.5 million parsecs away). The detection of three-megaelectronvolt photons provides evidence for the relativistic motion of the emitting plasma. Radiation from such rapidly moving gas around a rotating magnetar may have generated the rapid spectral evolution that we observe.