The first test of lepton flavor universality between muons and electrons using B^{+}→K^{+}π^{+}π^{-}ℓ^{+}ℓ^{-} (ℓ=e, μ) decays is presented. The measurement is performed with data from proton-proton collisions collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb^{-1}. The ratio of branching fractions between B^{+}→K^{+}π^{+}π^{-}e^{+}e^{-} and B^{+}→K^{+}π^{+}π^{-}μ^{+}μ^{-} decays is measured in the dilepton invariant-mass-squared range 1.1<q^{2}<7.0 GeV^{2}/c^{4} and is found to be R_{Kππ}^{-1}=1.31_{-0.17}^{+0.18}(stat) _{-0.09}^{+0.12}(syst), in agreement with the standard model prediction. The first observation of the B^{+}→K^{+}π^{+}π^{-}e^{+}e^{-} decay is also reported.