A search for invisible decays of a Higgs boson is performed using proton-proton collision data at 13 TeV collected with the CMS detector at the LHC in 2016, corresponding to an integrated luminosity of 35.9 fb. The search targets the production of a Higgs boson via vector boson fusion. The data are found to be in agreement with the background contributions from standard model processes. An observed (expected) upper limit of 0.33 (0.25), at 95% confidence level, is placed on the branching fraction of the standard model Higgs boson decay to invisible particles. The result from this analysis is combined with the ones from other searches for invisible decays of the Higgs boson performed using the 2016 data set. An observed (expected) upper limit of 0.26 (0.20), at 95% confidence level, is placed on the branching fraction of invisible decays of the Higgs boson, assuming standard model production rates. The combined expected result represents the most sensitive search for invisible decays of the Higgs boson to date. The result is also interpreted in the context of Higgs-portal dark matter models, in which upper bounds are placed on the spin-independent dark-matter-nucleon scattering cross section.