Abstract: The associated production of a Z boson or an off-shell photon γ* with a bottom quark in the forward region is studied using proton-proton collisions at a centre-of-mass energy of 7 TeV. The Z bosons are reconstructed in the Z/γ* → μ+μ− final state from muons with a transverse momentum larger than 20 GeV, while two transverse momentum thresholds are considered for jets (10 GeV and 20 GeV). Both muons and jets are reconstructed in the pseudorapidity range 2.0 < η < 4.5. The results are based on data corresponding to 1.0 fb−1 recorded in 2011 with the LHCb detector. The measurement of the Z+b-jet cross-section is normalized to the Z+jet cross-section. The measured cross-sections are(Formula presented.)for pT(jet) > 10 GeV, and(Formula presented.)for pT(jet) > 20 GeV.[Figure not available: see fulltext.].