A search for the standard model Higgs boson (H) decaying to bb¯ when produced in association with weak vector bosons (V) is reported for the following modes: W(μν)H, W(eν)H, Z(μμ)H, Z(ee)H and Z(νν)H. The search is performed in a data sample corresponding to an integrated luminosity of 4.7 fb−1, recorded by the CMS detector in proton–proton collisions at the LHC with a center-of-mass energy of 7 TeV. No significant excess of events above the expectation from background is observed. Upper limits on the VH production cross section times the H→bb¯ branching ratio, with respect to the expectations for a standard model Higgs boson, are derived for a Higgs boson in the mass range 110–135 GeV. In this range, the observed 95% confidence level upper limits vary from 3.4 to 7.5 times the standard model prediction; the corresponding expected limits vary from 2.7 to 6.7 times the standard model prediction.