We report on systematic temperature- and magnetic field-dependent studies of the EuGa₄ binary compound, which crystallizes in a centrosymmetric tetragonal BaAl₄-type structure with space group I4/mmm. The electronic properties of EuGa₄ single crystals, with an antiferromagnetic (AFM) transition at T_N ∼ 16.4 K, were characterized via electrical resistivity and magnetization measurements. A giant nonsaturating magnetoresistance was observed at low temperatures, reaching % at 2 K in a magnetic field of 9 T. In the AFM state, EuGa₄ undergoes a series of metamagnetic transitions in an applied magnetic field, clearly manifested in its field-dependent electrical resistivity. Below T_N, in the ∼4–7 T field range, we observe also a clear hump-like anomaly in the Hall resistivity which is part of the anomalous Hall resistivity. We attribute such a hump-like feature to the topological Hall effect, usually occurring in noncentrosymmetric materials known to host topological spin textures (as e.g., magnetic skyrmions). Therefore, the family of materials with a tetragonal BaAl₄-type structure, to which EuGa₄ and EuAl₄ belong, seems to comprise suitable candidates on which one can study the interplay among correlated-electron phenomena (such as charge-density wave or exotic magnetism) with topological spin textures and topologically nontrivial bands.