  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 TeV with
an integrated luminosity of 3.2 fb$^{-1}$. 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 underlying-event
models. The Monte Carlo model predictions qualitatively describe the data well,
but with some significant discrepancies.
