The differential branching fraction of the decay $Lambda_b^0rightarrowLambdamu^+mu^-$ is measured as a function of the square of the dimuon invariant mass, $q^2$. A yield of $78pm12$ $Lambda_b^0rightarrowLambdamu^+mu^-$ decays is observed using data, corresponding to an integrated luminosity of 1.0,fb$^{-1}$, collected by the LHCb experiment at a centre-of-mass energy of 7,TeV. A significant signal is found in the $q^2$ region above the square of the $J/psi$ mass, while at lower-$q^2$ values upper limits are set on the differential branching fraction. Integrating the differential branching fraction over $q^2$, while excluding the $J/psi$ and $psi(2S)$ regions, gives a branching fraction of $BF($Lambda_b^0rightarrowLambdamu^+mu^-$)=(0.96pm 0.16statpm 0.13systpm 0.21 (mathrm{norm}))times 10^{-6}$, where the uncertainties are statistical, systematic and due to the normalisation mode, $$Lambda_b^0rightarrow J/psiLambda$, respectively.
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