We report the first evidence for X(3872) production in two-photon interactions by tagging either the electron or the positron in the final state, exploring the highly virtual photon region. The search is performed in e+e-→e+e-J/ψ π+ π-, using 825 fb-1 of data collected by the Belle detector operated at the KEKB e+e-collider. We observe three X(3872) candidates, where the expected background is 0.11±0.10 events, with a significance of 3.2σ. We obtain an estimated value for γB(X(3872)→J/ψ π+ π-) assuming the Q2 dependence predicted by a cc meson model, where-Q2 is the invariant mass squared of the virtual photon. No X(3915)→J/ψ π+ π-candidates are found.