This Letter presents the results of a direct search with the ATLAS detector at the LHC for a Standard Model Higgs boson of mass 110⩽mH⩽130 GeV produced in association with a W or Z boson and decaying to bb¯. Three decay channels are considered: ZH→ℓ+ℓ−bb¯ WH→ℓνbb¯ and ZH→νν¯bb¯ where ℓ corresponds to an electron or a muon. No evidence for Higgs boson production is observed in a dataset of 7 TeV pp collisions corresponding to 4.7 fb−1 of integrated luminosity collected by ATLAS in 2011. Exclusion limits on Higgs boson production, at the 95% confidence level, of 2.5 to 5.5 times the Standard Model cross section are obtained in the mass range 110–130 GeV. The expected exclusion limits range between 2.5 and 4.9 for the same mass interval.