We have studied the magnetic structure of a Cr-doped iron-arsenide compound CaFe_{4}As_{3} by means of single crystal neutron diffraction. The neutron data reveal that below 90 K, an antiferromagnetic structure with propagation vector k=0 is adopted. Refinement of the magnetic structure using one of the modes allowed by symmetry analysis indicates that two of the four Fe sites, including the one where the selective substitution Fe/Cr happens, bear reduced magnetic moments. Density functional theory calculations confirm the stability of such a magnetic arrangement.