Summary: We introduce motivic zeta functions for matroids. These zeta functions are defined as sums over the lattice points of Bergman fans, and in the realizable case, they coincide with the motivic Igusa zeta functions of hyperplane arrangements. We show that these motivic zeta functions satisfy a functional equation arising from matroid Poincaré duality in the sense of Adiprasito-Huh-Katz [K. Adiprasito et al., Ann. Math. (2) 188, No. 2, 381–452 (2018; Zbl 1442.14194)]. In the process, we obtain a formula for the Hilbert series of the cohomology ring of a matroid, in the sense of E. M. Feichtner and S. Yuzvinsky [Invent. Math. 155, No. 3, 515–536 (2004; Zbl 1083.14059)]. We then show that our motivic zeta functions specialize to the topological zeta functions for matroids introduced by R. van der Veer [Discrete Math. 342, No. 9, 2680–2693 (2019; Zbl 1421.32036)], and we compute the first two coefficients in the Taylor expansion of these topological zeta functions, providing affirmative answers to two questions posed by van der Veer [loc. cit.].