This article presents measurements of tt¯ differential cross-sections in a fiducial phase-space region, using an integrated luminosity of 3.2 fb-1 of proton–proton data at a centre-of-mass energy of √s=13 TeV recorded by the ATLAS experiment at the LHC in 2015. Differential cross-sections are measured as a function of the transverse momentum and absolute rapidity of the top quark, and of the transverse momentum, absolute rapidity and invariant mass of the tt¯ system. The tt¯ events are selected by requiring one electron and one muon of opposite electric charge, and at least two jets, one of which must be tagged as containing a b-hadron. The measured differential cross-sections are compared to predictions of next-to-leading order generators matched to parton showers and the measurements are found to be consistent with all models within the experimental uncertainties with the exception of the Powheg-Box+ Herwig++ predictions, which differ significantly from the data in both the transverse momentum of the top quark and the mass of the tt¯ system.