A measurement of charged-particle distributions sensitive to the properties of the underlying event is presented for an inclusive sample of events containing a Z-boson , decaying to an electron or muon pair. The measurement is based on data collected using the ATLAS detector at the LHC in proton-proton collisions at a centre-of-mass energy of 7 TeV with an integrated luminosity of $4.6$ fb$^{-1}$. Distributions of the charged particle multiplicity and of the charged particle transverse momentum are measured in regions of azimuthal angle defined with respect to the Z-boson direction. The measured distributions are compared to similar distributions measured in jet events, and to the predictions of various Monte Carlo generators implementing different underlying event models.