  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 $2.0 < \eta < 4.5$ with transverse momenta $p_{T} > 20$
GeV/c. The dimuon mass is restricted to $60 < M_{\mu^{+}\mu^{-}} < 120$
GeV/c$^{2}$. The measured cross-section is
$$\sigma_{Z\rightarrow\mu^{+}\mu^{-}} = (76.0 \pm 0.3 \pm 0.5 \pm 1.0 \pm 1.3)
\, \text{pb}$$ 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
$$\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}} +
\sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{-}}}
= 20.63\pm0.09\pm0.12\pm0.05,$$ where the uncertainty due to luminosity
cancels.
