We have investigated the magnetic ground state of the antiferromagnetic Kondo-lattice compounds CeMAl$_{4}$Si$_{2}$ (M = Rh, Ir) using neutron powder diffraction. Although both of these compounds show two magnetic transitions $T_{N1}$ and $T_{N2}$ in the bulk properties measurements, evidence for magnetic long-range order was only found below the lower transition $T_{N2}$. Analysis of the diffraction profiles reveals a commensurate antiferromagnetic structure with a propagation vector $𝐤$= (0, 0, 1/2). The magnetic moment in the ordered state of CeRhAl$_{4}$Si$_{2}$ and CeIrAl$_{4}$Si$_{2}$ were determined to be 1.14(2) and 1.41(3) $μ_{B}$/Ce, respectively, and are parallel to the crystallographic $c$-axis in agreement with magnetic susceptibility measurements.