Strongly conducting or magnetized obstacles in a flowing plasma generate structures called Alfvén wings, which mediate momentum transfer between the obstacle and the plasma. Nonconducting obstacles such as airless planetary bodies can generate such structures, which, however, have so far been seen only in sub‐Alfvénic regime. A novel statistical analysis of simultaneous measurements made by two ARTEMIS satellites, one in the solar wind upstream of the Moon and one in the downstream wake, and comparison of the data with results of a three‐dimensional hybrid model of the interaction reveal that the perturbed plasma downstream of the Moon generates Alfvén wings in super‐Alfvénic solar wind. In the wake region, magnetic field lines bulge toward the Moon and the plasma flows are significantly perturbed. We use the simulation to show that some of the observed bends of the field result from field‐aligned currents. The perturbations in the wake thus arise from a combination of compressional and Alfvénic perturbations. Because of the super‐Alfvénic background flow of the solar wind, the two Alfvén wings fold back to form a small intersection angle. The currents that form the Alfvén wing in the wake are driven by both plasma flow deceleration and a gradient of plasma pressure, positive down the wake from the region just downstream of the Moon. Such Alfvén wing structures, caused by pressure gradients in the wake and the resulting plasma slowdown, should exist downstream of any nonconducting body in a super‐Alfvénic plasma flow.