Using a data sample of (1310.6±7.0)×106 J/ψ decay events collected with the BESIII detector at BEPCII, we study the electromagnetic Dalitz decay J/ψ→η′e+e- with two dominant η′ decay modes, η′→γπ+π- and η′→π+π-η. The branching fraction is determined to be B(J/ψ→η′e+e-)=(6.59±0.07±0.17)×10-5, which improves in precision by a factor of 2 over the previous BESIII measurement. A search for the dark photon (γ′) is performed via J/ψ→η′γ′, γ′→e+e-. Excluding the ω and φ mass regions, no significant signal is observed in the mass range from 0.1 to 2.1 GeV/c2. We set upper limits at the 90% confidence level on B(J/ψ→η′γ′)×B(γ′→e+e-), B(J/ψ→η′γ′) and the mixing strength as a function of dark photon mass. This is among the first searches for dark photons in charmonium decays.