The cross-section for the production of two jets in association with a leptonically decaying Z boson (Zjj) is measured in proton–proton collisions at a centre-of-mass energy of 13 TeV, using data recorded with the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 3.2 fb−1. The electroweak Zjj cross-section is extracted in a fiducial region chosen to enhance the electroweak contribution relative to the dominant Drell–Yan Zjj process, which is constrained using a data-driven approach. The measured fiducial electroweak cross-section is σEW Zjj = 119±16(stat.)±20(syst.)±2(lumi.) fb for dijet invariant mass greater than 250 GeV, and 34.2±5.8(stat.)±5.5(syst.)±0.7(lumi.) fb for dijet invariant mass greater than 1 TeV. Standard Model predictions are in agreement with the measurements. The inclusive Zjj cross-section is also measured in six different fiducial regions with varying contributions from electroweak and Drell–Yan Zjj production.