  The branching fraction of the rare decay $\Lambda_{b}^{0}\to \Lambda(1520)
\mu^{+}\mu^{-}$ is measured for the first time, in the squared dimuon mass
intervals, $q^2$, excluding the $J/\psi$ and $\psi(2S)$ 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 $9\
\mathrm{fb}^{-1}$. The result in the highest $q^{2}$ interval, $q^{2} >15.0\
\mathrm{GeV}^2/c^4$, where theoretical predictions have the smallest model
dependence, agrees with the predictions.
