Motivated by experiments on La2-x Bax CuO4 which suggest that stripe order coexists with two-dimensional pairing without interlayer phase coherence, we determine the interlayer Josephson coupling in the presence of stripe order. We employ a mean-field description of bond-centered stripes, with a zero-momentum superconducting condensate and alternating stripe directions pinned by the low-temperature tetragonal (LTT) lattice structure. We show that the Fermi-surface reconstruction arising from strong stripe order can suppress the Josephson coupling between adjacent layers by more than an order of magnitude.