We report the results of a search for the rare, purely leptonic decay B^{-}→μ^{-}ν[over ¯]_{μ} performed with a 711 fb^{-1} data sample that contains 772×10^{6} BB[over ¯] pairs, collected near the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} 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 B(B^{-}→μ^{-}ν[over ¯]_{μ})=(6.46±2.22±1.60)×10^{-7} or a frequentist 90% confidence level interval on the B^{-}→μ^{-}ν[over ¯]_{μ} branching fraction of [2.9,10.7]×10^{-7}.