The production of b jets in association with a Z/gamma* boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7TeV and recorded by the CMS detector. The inclusive cross section for Z/gamma* + b-jet production is measured in a sample corresponding to an integrated luminosity of 2.2 fb(-1). The Z/gamma* + b-jet cross section with Z/gamma* -> ll (where ll = ee or mu mu) 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 vertical bar eta vertical bar < 2.1, and a separation between the leptons and the jets of Delta R > 0.5 is found to be 5.84 +/- 0.08 (stat.) +/- 0.72 (syst.)(-0.55)(+0.25) (theory) pb. The kinematic properties of the events are also studied and found to be in agreement with the predictions made by the MADGRAPH event generator with the parton shower and the hadronisation performed by PYTHIA.