A first search is reported for a standard model Higgs boson ($H$) that is produced through vector boson fusion and decays to a bottom-quark pair. Two data samples, corresponding to integrated luminosities of $19.8\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ and $18.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of proton-proton collisions at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ were selected for this channel at the CERN LHC. The observed significance in these data samples for a $H\ensuremath{\rightarrow}b\overline{b}$ signal at a mass of 125 GeV is 2.2 standard deviations, while the expected significance is 0.8 standard deviations. The fitted signal strength $\ensuremath{\mu}=\ensuremath{\sigma}/{\ensuremath{\sigma}}_{\mathrm{SM}}=2.{8}_{\ensuremath{-}1.4}^{+1.6}$. The combination of this result with other CMS searches for the Higgs boson decaying to a $b$-quark pair yields a signal strength of $1.0\ifmmode\pm\else\textpm\fi{}0.4$, corresponding to a signal significance of 2.6 standard deviations for a Higgs boson mass of 125 GeV.