We report a search for Higgs bosons that are produced via vector boson fusion and subsequently decay into invisible particles. The experimental signature is an energetic jet pair with invariant mass of $\mathcal{O}(1) $ TeV and $\mathcal{O}(100) $ GeV missing transverse momentum. The analysis uses 36.1 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ of $pp$ collision data at $s=13$ TeV recorded by the ATLAS detector at the LHC. In the signal region the 2252 observed events are consistent with the background estimation. Assuming a 125 GeV particle with Standard Model cross sections, the upper limit on the branching fraction of the Higgs boson decay into invisible particles is 0.37 at 95% CL where 0.28 was expected. This limit is interpreted in Higgs portal models to set limits on the WIMP-nucleon scattering cross section. We also consider invisible decays of additional scalar bosons with masses up to 3 TeV for which the upper limits on the cross section times branching fraction are in the range of $0.3-1.7$ pb.