The quadrupolar out‐of‐plane Hall magnetic field generated during collisionless reconnection propagates away from the x line as a kinetic Alfvén wave (KAW). While it has been shown that this KAW carries substantial Poynting flux and propagates super‐Alfvenically, how this KAW damps as it propagates away from the x line is not well understood. In this study, this damping is examined using kinetic particle‐in‐cell simulations of antiparallel symmetric magnetic reconnection in a one‐dimensional current sheet equilibrium. In the reconnection simulations, the KAW wave vector has a typical magnitude comparable to an inverse fluid Larmor radius (effectively an inverse ion Larmor radius) and a direction of 85–89° relative to the local magnetic field. We find that the damping of the reconnection KAW is consistent with linear Landau damping results from a numerical Vlasov dispersion solver. This knowledge allows us to generalize our damping predictions to regions in the magnetotail and solar corona where the magnetic geometry can be approximated as a current sheet. For the magnetotail, the KAW from reconnection will not damp away before propagating the approximately 20 Earth radii associated with global magnetotail distances. For the solar corona, on the other hand, these KAWs will completely damp before reaching the distances comparable to the flare loop length. Key Points The quadrupolar out‐of‐plane magnetic field associated with reconnection propagates away from the x line as a kinetic Alfvén wave (KAW) The attenuation of this KAW is consistent with linear Landau damping theory For magnetotail plasma conditions, this KAW can propagate tens of Earth radii with little damping