This paper presents measurements of charged-particle distributions sensitive to the properties of the underlying event in events containing a Z boson decaying into a muon pair. The data were obtained using the ATLAS detector at the LHC in proton–proton collisions at a centre-of-mass energy of 13 Te-1. Distributions of the charged-particle multiplicity and of the charged-particle transverse momentum are measured in regions of the azimuth defined relative to the Z boson direction. The measured distributions are compared with the predictions of various Monte Carlo generators which implement different underyling event models. The Monte Carlo model predictions qualitatively describe the data well, but with some significant discrepancies.