A measurement of the production cross-section for Z bosons that decay to muons is presented. The data were recorded by the LHCb detector during pp collisions at a centre-of-mass energy of 7 TeV, and correspond to an integrated luminosity of 1.0 fb−1. The cross-section is measured for muons in the pseudorapidity range 2.0 < η < 4.5 with transverse momenta pT > 20 GeV/c. The dimuon mass is restricted to 60 < M μ + μ − < 120 GeV/c2. The measured cross-section is $$ {\sigma}_{Z\to \mu }{+}_{\mu }-=\left(76.0\pm 0.3\pm 0.5\pm 1.0\pm 1.3\right)\mathrm{p}\mathrm{b} $$ where the uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. This result is in good agreement with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. The cross-section is also measured differentially as a function of kinematic variables of the Z boson. Ratios of the production cross-sections of electroweak bosons are presented using updated LHCb measurements of W boson production. A precise test of the Standard Model is provided by the measurement of the ratio $$ \frac{\sigma_W{+}_{\to \mu +\nu \mu }+{\sigma}_{W^{-}\to {\mu}^{-}\overline{\nu}\mu }}{{\sigma_{Z\to \mu +}}_{\mu -}}=20.63\pm 0.09\pm 0.12\pm 0.05, $$ where the uncertainty due to luminosity cancels.