The Moon possesses strong magnetic anomalies that are enigmatic given the weak magnetism of lunar rocks. We show that the most prominent grouping of anomalies can be explained by highly magnetic extralunar materials from the projectile that formed the largest and oldest impact crater on the Moon: the South Pole-Aitken basin. The distribution of projectile materials from a model oblique impact coincides with the distribution of magnetic anomalies surrounding this basin, and the magnetic properties of these materials can account for the intensity of the observed anomalies if they were magnetized in a core dynamo field. Distal ejecta from this event can explain the origin of isolated magnetic anomalies far from this basin.