The magnetic correlations in the quasi-two-dimensional (2D) spin- ½ square-lattice system Zn₂VO(PO₄)₂ have been investigated by neutron-diffraction technique. A long-range antiferromagnetic (AFM) ordering below 3.75 K (T_N) has been observed with a reduced moment of 0.66 (2) µ_B per V ion at 1.5 K. In a given ab plane, the AFM spin arrangement is Néel type and the AFM layers are coupled ferromagnetically along the c axis. Remarkably, we have observed a pure 2D short-range AFM ordering in the ab plane above T_N. Interestingly, the coexistence of diffuse magnetic scattering and three-dimensional antiferromagnetic Bragg peaks has been found below T_N, indicating the presence of spin waves as confirmed by our calculation using the linear spin-wave theory. The observed results are discussed in the light of existing theory for a two-dimensional spin-  ½ square-lattice system.