A search is presented for excited electrons and muons in ℓℓγ final states at the LHC. The search is based on a data sample corresponding to an integrated luminosity of 35.9 fb^-1 of proton-proton collisions at a center-of-mass energy of 13 TeV, collected with the CMS detector in 2016. This is the first search for excited leptons at √s = 13 TeV. The observation is consistent with the standard model background prediction, and the most stringent exclusion limits to date are set on the excited lepton mass and the compositeness scale, at 95% confidence level. Excited electrons and muons are excluded for masses below 3.9 and 3.8 TeV, respectively, under the assumption that the excited lepton mass equals the compositeness scale. The best observed limit on the compositeness scale is obtained with an excited lepton mass of around 1.0 TeV, excluding values below 25 TeV for both excited electrons and muons.