Using electromagnetic hybrid (kinetic ions, fluid electrons) simulations, the interaction between solar wind and a magnetized asteroid is investigated. At no or very low levels of asteroid magnetization the solar wind remains undisturbed. As the level of magnetization is increased, a phase standing whistler wake is generated which owing to its propagation characteristics remains confined to planes close to that containing the solar wind flow velocity and the interplanetary magnetic field (IMF). No density perturbations are associated with this wake. Further increase in asteroid magnetization results in the additional generation of fast and slow magnetosonic wakes, which fall behind the whistler wake and are associated with the formation of a plasma tail. Because of their propagation characteristics, these wakes are more symmetric than the whistler wake. At still higher levels of magnetization where plasma pileup occurs upstream of the asteroid, the fast magnetosonic wake becomes dominant and eventually exhibits shock‐like behavior. In general, the size of the interaction region increases with the level of asteroid's magnetic field strength. This interaction region is highly structured and asymmetric owing to wave propagation characteristics and the IMF direction. In addition, once the fast magnetosonic wake is strong enough to result in ion reflection the subsequent E × B motion of these ions results in considerable asymmetry in the interaction region. This is a purely ion kinetic effect which comes about as a result of the overall interaction region being comparable to ion scale lengths.