A search for a standard model Higgs boson (H) that is produced through vector boson fusion and decays to a bottom-quark pair is performed using proton-proton collisions at $\sqrt{s}=13$~TeV. The data sample corresponds to an integrated luminosity of 2.3~fb$^{-1}$ recorded in 2015 with the CMS experiment at the CERN LHC. The observed 95\% confidence level upper limit on the production of a $\mathrm{H}\rightarrow \mathrm{b\overline{b}}$ signal at a mass of 125~GeV is 3.0 times the standard model expectation, compared to 5.0 expected in absence of a signal. The combination of this result with the previous CMS search using proton-proton collisions at $\sqrt{s}=8$~TeV yields an observed 95\% confidence level upper limit on the signal production of 3.4 times the standard model expectation, where 2.2 is expected in the absence of signal, and a corresponding fitted signal strength $\mu=\sigma/\sigma_\mathrm{SM}=1.3^{+1.2}_{-1.1}$.

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