A search for the $b\overline{b}$ decay of the Standard Model Higgs boson produced through vector-boson fusion is presented. Three mutually exclusive channels are considered: two all-hadronic channels and a photon-associated channel. Results are reported from the analysis of up to $30.6\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of $pp$ data at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ collected with the ATLAS detector at the LHC. The measured signal strength relative to the Standard Model prediction from the combined analysis is $2.{5}_{\ensuremath{-}1.3}^{+1.4}$ for inclusive Higgs boson production and $3.{0}_{\ensuremath{-}1.6}^{+1.7}$ for vector-boson fusion production only.