Inclusive J/ψ production is studied in minimum-bias proton-proton collisions at a centre-of-mass energy of 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 d²σ/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 〈pT2〉 are extracted and compared with results obtained at other collision energies. [Figure not available: see fulltext.].