Polymersomes, made up of amphiphilic block copolymers, are emerging as a powerful tool in drug delivery and synthetic biology due to their high stability, chemical versatility, and surface modifiability. The full potential of polymersomes, however, has been hindered by a lack of versatile methods for shape control. Here we show that a range of non-spherical polymersome morphologies with anisotropic membranes can be obtained by exploiting hydrophobic directional aromatic interactions between perylene polymer units within the membrane structure. By controlling the extent of solvation/desolvation of the aromatic side chains through changes in solvent quality, we demonstrate facile access to polymersomes that are either ellipsoidal or tubular-shaped. Our results indicate that perylene aromatic interactions have a great potential in the design of non-spherical polymersomes and other structurally complex self-assembled polymer structures.