A measurement of the Z(→ μ + μ −) + jet production cross-section in pp collisions at a centre-of-mass energy s√ = 7 TeV is presented. The analysis is based on an integrated luminosity of 1.0 fb−1 recorded by the LHCb experiment. Results are shown with two jet transverse momentum thresholds, 10 and 20 GeV, for both the overall cross-section within the fiducial volume, and for six differential cross-section measurements. The fiducial volume requires that both the jet and the muons from the Z boson decay are produced in the forward direction (2.0 < η < 4.5). The results show good agreement with theoretical predictions at the second-order expansion in the coupling of the strong interaction.