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Topological Dirac semimetals, systems containing low energy relativistic Dirac quasiparticle excitations, have received ample attention in condensed matter physics. Early work on Dirac semimetals focused on nonmagnetic systems with the presence of time reversal symmetry. Recent interest has turned toward the study of magnetic Dirac materials. Here, we have studied the transport and the electronic structure of  Eu-ternary pnictide EuMg₂Bi₂ by utilizing high-resolution angle-resolved photoemission spectroscopy (ARPES) which is supplemented by first-principles calculations. We have performed electrical resistivity, magnetization, and specific heat capacity measurements of EuMg₂Bi₂ and confirm the existence of antiferromagnetic ordering below the temperature of 6.7 K. Our ARPES measurement reveals the electronic structure of this system is dominated by linearly dispersive hole-like bands near the Fermi level. First principles calculations show excellent agreement with these observations. Furthermore, our results also suggest the presence of a single Dirac point above the experimental Fermi level. These findings give an opportunity to study the interplay between topology and magnetism.