Results are presented from two-dimensional hybrid simulations of the interaction of a supercritical quasi-perpendicular collisionless shock wave with current sheets embedded in the upstream flow. The current sheet normals are perpendicular to the shock normal. When the motional electric field is directed toward the discontinuity, the interaction leads to the generation of a region with high ion temperature, low magnetic field, and low density, which has many properties of a class of events variously referred to as active current sheets, hot diamagnetic cavities, or hot flow anomalies (HFAs). The simulations demonstrate that the HFA rsults from the interaction of ions reflected at the shock with the current sheet. The interaciton does not involve an instability and is not caused by the collision of the current sheet and the shock but rather is a property of a shock with an embedded current sheet. The simulations suggest that the HFAs formed in this way are always attached to the shock and extend into both the upstream and downstream regions.