The ZZ production cross section in proton-proton collisions at 13 TeV center-of-mass energy is measured using 3.2 fb-1 of data recorded with the ATLAS detector at the Large Hadron Collider. The considered Z boson candidates decay to an electron or muon pair of mass 66-116 GeV. The cross section is measured in a fiducial phase space reflecting the detector acceptance. It is also extrapolated to a total phase space for Z bosons in the same mass range and of all decay modes, giving 16.7-2.0+2.2(stat)+0.9-0.7(syst)+1.0-0.7(lumi) pb. The results agree with standard model predictions.