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 sigma(Zjj)(EW) = 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.