  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 Poincar\'{e} duality in the sense of
Adiprasito-Huh-Katz. In the process, we obtain a formula for the Hilbert series
of the cohomology ring of a matroid, in the sense of Feichtner-Yuzvinsky. We
then show that our motivic zeta functions specialize to the topological zeta
functions for matroids introduced by van der Veer, 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.
