A search for supersymmetry is presented using a sample of events with b jets and missing transverse momentum. The search uses a data sample of proton-proton collisions at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 35 inverse picobarns, collected with the CMS detector. A total of 0.33 +0.43 -0.33 (stat.) +/- 0.13 (syst.) events is predicted, using control samples in the data, to arise from standard model processes, and one event is observed in the data. Upper limits are set at the 95% confidence level on the cross sections of benchmark supersymmetric models.