Abstract We predict a repulsive Casimir–Polder-type dispersion interaction between a single neutron and a metal or dielectric surface. We consider a scenario where a single neutron is subject to an external magnetic field. Due to its intrinsic magnetic moment, the neutron then forms a magnetisable two-level system which can exchange virtual photons with a nearby surface. The resulting dispersion interaction between a purely magnetic object (neutron) and a purely electric one (surface) is found to be repulsive, in contrast to the typical attractive interaction between electric objects. Its magnitude is considerably smaller than the standard atom–surface Casimir–Polder force due to the magnetic nature of the interaction and the smallness of the electron-to-neutron mass ratio. Nevertheless, we show that it can be comparable to the gravitational potential of the same surface and should be taken into consideration in future neutron interference experiments.