Here we investigate antiferromagnetic Eu₅In₂Sb₆, a nonsymmorphic Zintl phase. Our electrical transport data show that Eu₅In₂Sb₆ is remarkably insulating and exhibits an exceptionally large negative magnetoresistance, which is consistent with the presence of magnetic polarons. From ab initio calculations, the paramagnetic state of Eu₅In₂Sb₆ is a topologically nontrivial semimetal within the generalized gradient approximation (GGA), whereas an insulating state with trivial topological indices is obtained using a modified Becke-Johnson potential. Notably, GGA + U calculations suggest that the antiferromagnetic phase of Eu₅In₂Sb₆ may host an axion insulating state. Our results provide important feedback for theories of topological classification and highlight the potential of realizing clean magnetic narrow-gap semiconductors in Zintl materials.