A search for excited electrons produced in pp collisions at s = 13 Te via a contact interaction qq¯ → ee∗ is presented. The search uses 36.1 fb- 1 of data collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider. Decays of the excited electron into an electron and a pair of quarks (eqq¯) are targeted in final states with two electrons and two hadronic jets, and decays via a gauge interaction into a neutrino and a W boson (νW) are probed in final states with an electron, missing transverse momentum, and a large-radius jet consistent with a hadronically decaying W boson. No significant excess is observed over the expected backgrounds. Upper limits are calculated for the pp→ ee∗→ eeqq¯ and pp→ ee∗→ eνW production cross sections as a function of the excited electron mass me∗ at 95% confidence level. The limits are translated into lower bounds on the compositeness scale parameter Λ of the model as a function of me∗. For me∗<0.5 Te, the lower bound for Λ is 11 Te. In the special case of me∗=Λ, the values of me∗<4.8 Te are excluded. The presented limits on Λ are more stringent than those obtained in previous searches.