Since their discovery in 2007(1), much effort has been devoted to uncovering the sources of the extragalactic, millisecond-duration fast radio bursts (FRBs)(2). A class of neutron stars known as magnetars is a leading candidate source of FRBs(3,4). Magnetars have surface magnetic fields in excess of 10(14) gauss, the decay of which powers a range of high-energy phenomena(5). Here we report observations of a millisecond-duration radio burst from the Galactic magnetar SGR 1935+2154, with a fluence of 1.5 +/- 0.3 megajansky milliseconds. This event, FRB 200428 (ST 200428A), was detected on 28 April 2020 by the STARE2 radio array(6) in the 1,281-1,468 megahertz band. The isotropic-equivalent energy released in FRB 200428 is 4 x 10(3) times greater than that of any radio pulse from the Crab pulsar-previously the source of the brightest Galactic radio bursts observed on similar timescales(7). FRB 200428 is just 30 times less energetic than the weakest extragalactic FRB observed so far(8), and is drawn from the same population as the observed FRB sample. The coincidence of FRB 200428 with an X-ray burst(9-11) favours emission models that describe synchrotron masers or electromagnetic pulses powered by magnetar bursts and giant flares(3,4,12,13). The discovery of FRB 200428 implies that active magnetars such as SGR 1935+2154 can produce FRBs at extragalactic distances. Observations of the fast radio burst FRB 200428 coinciding with X-rays from the Galactic magnetar SGR 1935+2154 indicate that active magnetars can produce fast radio bursts at extragalactic distances.