Inclusive J/ψ production is studied in minimum-bias proton-proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 5.02 TeV by ALICE at the CERN LHC. The measurement is performed at mid-rapidity (|y| < 0.9) in the dielectron decay channel down to zero transverse momentum p T, using a data sample corresponding to an integrated luminosity of L int = 19.4 ± 0.4 nb −1. The measured p T-integrated inclusive J/ψ production cross sec- tion is dσ/dy = 5.64 ± 0.22(stat.) ± 0.33(syst.) ± 0.12(lumi.) μb. The p T-differential cross section d2 σ/dp Tdy is measured in the p T range 0–10 GeV/c and compared with state-of- the-art QCD calculations. The J/ψ 〈p T〉 and $\left({p}_{T}^{2}\right)$ are extracted and compared with results obtained at other collision energies.