A measurement of the production cross-section of Z bosons in pp collisions at $sqrt{s} = 13$ TeV is presented using dimuon and dielectron final states in LHCb data. The cross-section is measured for leptons with pseudorapidities in the range $2.0 < eta < 4.5$, transverse momenta $p_text{T} > 20$ GeV and dilepton invariant mass in the range $60<m(ellell)<120$ GeV. The integrated cross-section from averaging the two final states is begin{equation*}sigma_{text{Z}}^{ellell} = 194.3 pm 0.9 pm 3.3 pm 7.6text{ pb,}end{equation*} where the first uncertainty is statistical, the second is due to systematic effects, and the third is due to the luminosity determination. In addition, differential cross-sections are measured as functions of the Z boson rapidity, transverse momentum and the angular variable $phi^*_eta$.