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/e. The dimuon mass is restricted to 60 < M mu+mu- < 120 GeV/c(2). The measured cross-section is sigma(Z ->mu+mu-) = (76.0 +/- 0.3 +/- 0.5 +/- 1.0 +/- 1.3) 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 sigma(W+) -> mu(+) nu(mu) + sigma(W) -> mu(+) (nu) over bar (mu)/sigma(Z ->mu+mu-) = 0.09 +/- 0.12 +/- 0.05, where the uncertainty due to luminosity cancels.