The recent demonstration of topological states in antiferromagnets (AFMs) provides an exciting platform for exploring prominent physical phenomena and applications of antiferromagnetic spintronics. A famous example is the AFM topological insulator (TI) state, which, however, was still not observed in two dimensions. Using a tight-binding model and first-principles calculations, we show that, in contrast to previously observed AFM topological insulators in three dimensions, an AFM TI can emerge in two dimensions as a result of a nonsymmorphic symmetry that combines the twofold rotation symmetry and half-lattice translation. Based on the spin Chern number, Wannier charge centers, and gapless edge states analysis, we identify intrinsic AFM XMnY (X=Sr and Ba, Y=Sn and Pb) quintuple layers as experimentally feasible examples of predicted topological states with a stable crystal structure and giant magnitude of the nontrivial band gaps, reaching as much as 186meV for SrMnPb, thereby promoting these systems as promising candidates for innovative spintronics applications.