In the 1980s, excess infrared emission was discovered around main-sequence stars; subsequent direct-imaging observations revealed orbiting disks of cold dust to be the source. These `debris disks' were thought to be by-products of planet formation because they often exhibited morphological and brightness asymmetries that may result from gravitational perturbation by planets. This was proved to be true for the β Pictoris system, in which the known planet generates an observable warp in the disk. The nearby, young, unusually active late-type star AU Microscopii hosts a well-studied edge-on debris disk; earlier observations in the visible and near-infrared found asymmetric localized structures in the form of intensity variations along the midplane of the disk beyond a distance of 20 astronomical units. Here we report high-contrast imaging that reveals a series of five large-scale features in the southeast side of the disk, at projected separations of 10-60 astronomical units, persisting over intervals of 1-4 years. All these features appear to move away from the star at projected speeds of 4-10 kilometres per second, suggesting highly eccentric or unbound trajectories if they are associated with physical entities. The origin, localization, morphology and rapid evolution of these features are difficult to reconcile with current theories.