We report the results of a search for the rare, purely leptonic decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ performed with a $711\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data sample that contains $772\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }B\overline{B}$ pairs, collected near the $\mathrm{\ensuremath{\Upsilon}}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. The signal events are selected based on the presence of a high momentum muon and the topology of the rest of the event showing properties of a generic $B$-meson decay, as well as the missing energy and momentum being consistent with the hypothesis of a neutrino from the signal decay. We find a 2.4 standard deviation excess above background including systematic uncertainties, which corresponds to a branching fraction of $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})=(6.46\ifmmode\pm\else\textpm\fi{}2.22\ifmmode\pm\else\textpm\fi{}1.60)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ or a frequentist 90% confidence level interval on the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ branching fraction of $[2.9,10.7]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.