Given an irreducible, end-periodic homeomorphism f:S→Sf:S→S of a surface with finitely many ends, all accumulated by genus, the mapping torus, MfMf, is the interior of a compact, irreducible, atoroidal 3-manifold M¯føverlineMf with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of M¯føverlineMf in terms of the translation length of ff on the pants graph of SS. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.