X-ray magnetic circular dichroism (XMCD) measurements on single-crystal and powder samples of Ba$_{0.6}$K$_{0.4}$Mn$_{2}$As$_{2}$ show that the ferromagnetism below $T_{textrm{C}}approx$ 100 K arises in the As $4p$ conduction band. No XMCD signal is observed at the Mn x-ray absorption edges. Below $T_{textrm{C}}$, however, a clear XMCD signal is found at the As $K$ edge which increases with decreasing temperature. The XMCD signal is absent in data taken with the beam directed parallel to the crystallographic $textrm{c}$ axis indicating that the orbital magnetic moment lies in the basal plane of the tetragonal lattice. These results show that the previously reported itinerant ferromagnetism is associated with the As $4p$ conduction band and that distinct local-moment antiferromagnetism and itinerant ferromagnetism with perpendicular easy axes coexist in this compound at low temperature.