The spin Hall effect (SHE)1–5 achieves coupling between charge currents and collective spin dynamics in magnetically ordered systems and is a key element of modern spintronics6–9. However, previous research has focused mainly on non-magnetic materials, so the magnetic contribution to the SHE is not well understood. Here we show that antiferromagnets have richer spin Hall properties than do non-magnetic materials. We find that in the non-collinear antiferromagnet10 Mn3Sn, the SHE has an anomalous sign change when its triangularly ordered moments switch orientation. We observe contributions to the SHE (which we call the magnetic SHE) and the inverse SHE (the magnetic inverse SHE) that are absent in non-magnetic materials and that can be dominant in some magnetic materials, including antiferromagnets. We attribute the dominance of this magnetic mechanism in Mn3Sn to the momentum-dependent spin splitting that is produced by non-collinear magnetic order. This discovery expands the horizons of antiferromagnet spintronics and spin–charge coupling mechanisms.