Using the data on coherent J/ψ photoproduction in Pb-Pb ultraperipheral collisions (UPCs) obtained in Runs 1 and 2 at the Large Hadron Collider (LHC), we determined with a good accuracy the nuclear suppression factor of SPb(x) in a wide range of the momentum fraction x, 10−5≤x≤0.04. In the small-x region x<10−3, our χ2 fit favors a flat form of SPb(x)≈0.6 with approximately a 5% accuracy for x=6×10−4−10−3 and a 25% error at x=10−4. At the same time, uncertainties of the fit do not exclude a slow decrease of SPb(x) in the small-x limit. At large x, SPb(x) is constrained to better than 10% precision up to x=0.04 and is also consistent with the value of SPb(x) at 〈x〉=0.042, which we extract from the Fermilab data on the A dependence of the cross section of coherent J/ψ photoproduction on fixed nuclear targets. The resulting uncertainties on SPb(x) are small, which indicates the potential of the LHC data on coherent charmonium photoproduction in Pb-Pb UPCs to provide additional constraints on small-x nPDFs. We explicitly demonstrate this using as an example the EPPS16 and nCTEQ16 nuclear parton distribution functions, whose uncertainties decrease severalfold after the Bayesian reweighting of the discussed UPC data.