A search for the lepton-flavour violating decay D0→e±μ∓ is made with a dataset corresponding to an integrated luminosity of View the MathML source of proton–proton collisions at centre-of-mass energies of View the MathML source and View the MathML source, collected by the LHCb experiment. Candidate D0 mesons are selected using the decay D⁎+→D0π+ and the D0→e±μ∓ branching fraction is measured using the decay mode D0→K−π+ as a normalization channel. No significant excess of D0→e±μ∓ candidates over the expected background is seen, and a limit is set on the branching fraction, B(D0→e±μ∓)<1.3×10−8, at 90% confidence level. This is an order of magnitude lower than the previous limit and it further constrains the parameter space in some leptoquark models and in supersymmetric models with R-parity violation.