Using (1310.6±7.0)×106 J/ψ events acquired with the BESIII detector at the BEPCII storage rings, the decay η′→π+π-μ+μ- is observed for the first time with a significance of 8σ via the process J/ψ→γη′. We measure the branching fraction of η′→π+π-μ+μ- to be B(η′→π+π-μ+μ-)=(1.97±0.33(stat)±0.19(syst))×10-5, where the first and second uncertainties are statistical and systematic, respectively. © 2021 authors. Published by the American Physical Society.