We argue that with an increase of the collision energy, elastic photoproduction of ρ mesons on nuclei becomes affected by the significant cross section of photon inelastic diffraction into large masses, which results in the sizable inelastic nuclear shadowing correction to σγA→ρA and the reduced effective ρ-nucleon cross section. We take these effects into account by combining the vector meson dominance model, which we upgrade to include the contribution of high-mass fluctuations of the photon according to QCD constraints, and the Gribov–Glauber approximation for nuclear shadowing, where the inelastic nuclear shadowing is included by means of cross section fluctuations. The resulting approach allows us to successfully describe the data on elastic ρ photoproduction on nuclei in heavy ion UPCs in the 7 GeV<Wγp<46 GeV energy range and to predict the value of the cross section of coherent ρ photoproduction in Pb–Pb UPCs at sNN=5.02 TeV in Run 2 at the LHC, dσPbPb→ρPbPb(y=0)/dy=560±25 mb.