The disorder dependence of the oxygen isotope effect in optimally doped Bi2Sr1.6Ln0.4CuO6+δ superconductors which is introduced into cation sites in the planes adjacent to CuO2 planes is studied. The degree of out-of-plane disorder is controlled by substituting Ln ions with different ionic radii from La to Gd. This type of disorder does not explicitly alter the nodal electronic structure or the underlying Fermi surface but markedly enhances the oxygen isotope exponent at the superconducting transition temperature (αTc). The enhancement in αTc is well explained by the pair-breaking model, suggesting the growth of a pseudogap state around the antinodal region due to the out-of-plane disorder.