Using a data set of 2.93 fb−1 taken at a center-of-mass energy of with the BESIII detector at the BEPCII collider, we measure the process e+e−→J/ψγ→μ+μ−γ and determine the product of the branching fraction and the electronic width Bμμ⋅Γee=(333.4±2.5stat±4.4sys) eV. Using the earlier-published BESIII result for Bμμ=(5.973±0.007stat±0.037sys)%, we derive the J/ψ electronic width Γee=(5.58±0.05stat±0.08sys) keV.