The branching fraction ratio R(D^{*})≡B(B[over ¯]^{0}→D^{*+}τ^{-}ν[over ¯]_{τ})/B(B[over ¯]^{0}→D^{*+}μ^{-}ν[over ¯]_{μ}) is measured using a sample of proton-proton collision data corresponding to 3.0 fb^{-1} of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode τ^{-}→μ^{-}ν[over ¯]_{μ}ν_{τ}. The semitauonic decay is sensitive to contributions from non-standard-model particles that preferentially couple to the third generation of fermions, in particular, Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate B[over ¯]^{0} decays gives R(D^{*})=0.336±0.027(stat)±0.030(syst). This result, which is the first measurement of this quantity at a hadron collider, is 2.1 standard deviations larger than the value expected from lepton universality in the standard model.