In this paper we consider a massive vector field in the background of a space-time obtained by certain Z2 quotient of the Banados-Teitelboim-Zanelli black hole. We analyze the backreaction of the matter field on the space-time geometry up to first order in metric perturbation. The expectation value of the stress-energy tensor can be computed exactly by considering its pullback onto the covering space. Upon a suitable choice of the boundary condition on the vector field around a noncontractible cycle of the quotient manifold it is possible to obtain the average energy on a null geodesic to be negative there by resulting a traversable wormhole. © 2020 authors. Published by the American Physical Society.