Proton-γ coincidences from (d,p) reactions between a Ni66 beam and a deuterated polyethylene target have been analyzed with the inverse-Oslo method to find the nuclear level density (NLD) and γ-ray strength function (γSF) of Ni67. The Ni66(n,γ) capture cross section has been calculated using the Hauser-Feshbach model in TALYS using the measured NLD and γSF as constraints. The results confirm that the Ni66(n,γ) reaction acts as a bottleneck when relying on one-zone nucleosynthesis calculations. However, the impact of this reaction is strongly dampened in multizone models of low-metallicity AGB stars experiencing i-process nucleosynthesis.