Spatial inversion symmetry in crystal structures is closely related to the superconducting (SC) and magnetic properties of materials. Recently, several theoretical proposals that predict various interesting phenomena caused by the breaking of the local inversion symmetry have been presented. However, experimental validation has not yet progressed owing to the lack of model materials. Here we present evidence for antiferromagnetic (AFM) order in CeRh_{2}As_{2} (SC transition temperature T_{SC}∼0.37 K), wherein the Ce site breaks the local inversion symmetry. The evidence is based on the observation of different extents of broadening of the nuclear quadrupole resonance spectrum at two crystallographically inequivalent As sites. This AFM ordering breaks the inversion symmetry of this system, resulting in the activation of an odd-parity magnetic multipole. Moreover, the onset of antiferromagnetism T_{N} within an SC phase, with T_{N}<T_{SC}, is quite unusual in systems wherein superconductivity coexists or competes with magnetism. Our observations show that CeRh_{2}As_{2} is a promising system to study how the absence of local inversion symmetry induces or influences unconventional magnetic and SC states, as well as their interaction.