We report a search for Higgs bosons that are produced via vector boson fusion and subsequently decay into invisible particles. The experimental signature is two energetic jets with $\mathcal{O}(1)$ TeV invariant mass and $\mathcal{O}(100)$ GeV missing transverse momentum. The analysis uses 36.1 fb$^{-1}$ of $pp$ collision data at 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% confidence level 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 $0.3-2.0$ pb.

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