We report the result for a search for the leptonic decay of B+→μ+νμ using the full Belle dataset of 711 fb−1 of integrated luminosity at the ϒ(4S) resonance. In the Standard Model leptonic B-meson decays are helicity and Cabibbo-Kobayashi-Maskawa suppressed. To maximize sensitivity an inclusive tagging approach is used to reconstruct the second B meson produced in the collision. The directional information from this second B meson is used to boost the observed μ into the signal B-meson rest frame, in which the μ has a monochromatic momentum spectrum. Though its momentum is smeared by the experimental resolution, this technique improves the analysis sensitivity considerably. Analyzing the μ momentum spectrum in this frame we find B(B+→μ+νμ)=(5.3±2.0±0.9)×10−7 with a one-sided significance of 2.8 standard deviations over the background-only hypothesis. This translates to a frequentist upper limit of B(B+→μ+νμ)<8.6×10−7 at 90% confidence level. The experimental spectrum is then used to search for a massive sterile neutrino, B+→μ+N, but no evidence is observed for a sterile neutrino with a mass in a range of 0–1.5 GeV. The determined B+→μ+νμ branching fraction limit is further used to constrain the mass and coupling space of the type II and type III two-Higgs-doublet models.