The cross-section for the production of two jets in association with a leptonically decaying Z boson (Z$jj$) 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 Z$jj$ 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 $\sigma^{Zjj}_{EW}= 119\pm 16 (\mathrm{stat.}) \pm 20 (\mathrm{syst.})\pm 2 (\mathrm{lumi.})$ for dijet invariant mass greater than 250 GeV, and $34.2\pm 5.8 (\mathrm{stat.})\pm 5.5 (\mathrm{syst.})\pm 0.7 (\mathrm{lumi.})$ for dijet invariant mass greater than 1 TeV. Standard Model predictions are in agreement with the measurements. The inclusive Z$jj$ cross-section is also measured in six different fiducial regions with varying contributions from electroweak and Drell–Yan Z$jj$ production.