Magnetars are the most highly magnetized neutron stars in the cosmos (with magnetic field 10(13)-10(15) G). Giant flares from magnetars are rare, short-duration (about 0.1 s) bursts of hard X-rays and soft gamma rays(1,2). Owing to the limited sensitivity and energy coverage of previous telescopes, no magnetar giant flare has been detected at gigaelectronvolt (GeV) energies. Here, we report the discovery of GeV emission from a magnetar giant flare on 15 April 2020 (refs. (3,4) and A. J. Castro-Tirado et al., manuscript in preparation). The Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope detected GeV gamma rays from 19 s until 284 s after the initial detection of a signal in the megaelectronvolt (MeV) band. Our analysis shows that these gamma rays are spatially associated with the nearby (3.5 megaparsecs) Sculptor galaxy and are unlikely to originate from a cosmological gamma-ray burst. Thus, we infer that the gamma rays originated with the magnetar giant flare in Sculptor. We suggest that the GeV signal is generated by an ultra-relativistic outflow that first radiates the prompt MeV-band photons, and then deposits its energy far from the stellar magnetosphere. After a propagation delay, the outflow interacts with environmental gas and produces shock waves that accelerate electrons to very high energies; these electrons then emit GeV gamma rays as optically thin synchrotron radiation. This observation implies that a relativistic outflow is associated with the magnetar giant flare, and suggests the possibility that magnetars can power some short gamma-ray bursts.