  Using $(1310.6 \pm 7.0) \times 10^{6}~J/\psi$ events acquired with the BESIII
detector at the BEPCII storage rings, the decay
$\eta^\prime\rightarrow\pi^+\pi^-\mu^+\mu^-$ is observed for the first time
with a significance of 8$\sigma$ via the process
$J/\psi\rightarrow\gamma\eta'$. We measure the branching fraction of
$\eta^\prime\rightarrow\pi^+\pi^-\mu^+\mu^-$ to be
$\mathcal{B}(\eta^\prime\rightarrow\pi^+\pi^-\mu^+\mu^-)$=(1.97$\pm$0.33(stat.)$\pm$0.18(syst.))$\times10^{-5}$,
where the first and second uncertainties are statistical and systematic,
respectively.
