We examine statistically the magnetic field in the Venusian magnetotail which is formed by the draping of interplanetary magnetic field lines. Although the near‐planet and distant magnetotail regions have been sampled by the various missions to Venus and the general magnetic features of the distant magnetotail are well established, the near wake region from about 1.3 to 3 Venusian radii downstream of the planet remained unexplored until the Venus Express mission. Here we report the unanticipated finding of a draped field reversal in one hemisphere of the near Venus tail. When ordered by the interplanetary electric field orientation, the magnetic field lines in the hemisphere with inward motional electric field apparently are wrapped more tightly around Venus than in the other hemisphere, thus forming a field reversal region in the this portion of the near tail. A global hybrid simulation produces what we see and provides a three‐dimensional view of the observed hemispherical asymmetry.