The branching fraction of the rare decay Λ_{b}^{0}→Λ(1520)μ^{+}μ^{-} is measured for the first time, in the squared dimuon mass intervals q^{2}, excluding the J/ψ and ψ(2S) regions. The data sample analyzed was collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb^{-1}. The result in the highest q^{2} interval, q^{2}>15.0 GeV^{2}/c^{4}, where theoretical predictions have the smallest model dependence, agrees with the predictions.