The production of b jets in association with a Z/γ^* boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7 TeV and recorded by the CMS detector. The inclusive production rates for Z/γ^* + b-jet is measured in a sample corresponding to an integrated luminosity of 2.2 fb⁻¹ (inverse femtobarns). The Z/γ^* + b-jet production rate with Z/γ^* to ll (where ll = ee or μμ) for events with the invariant mass 60 M(ll) 120 GeV, at least one b jet at the hadron level with p_T > 25 GeV and |η| 2.1, and a separation between the leptons and the jets of ΔR > 0.5 is found to be 5.84 ± 0.08 (stat.) ± 0.72 (syst.) _−0.44^+0.25 (theory) pb. The kinematic properties of the events are also studied and found to be in agreement with predictions.