We report on a search for the standard-model Higgs boson in pp collisions at s√=1.96  TeV using an integrated luminosity of 2.0  fb−1. We look for production of the Higgs boson decaying to a pair of bottom quarks in association with a vector boson V (W or Z) decaying to quarks, resulting in a four-jet final state. Two of the jets are required to have secondary vertices consistent with B-hadron decays. We set the first 95% confidence level upper limit on the VH production cross section with V(→qq/qq′)H(→bb) decay for Higgs boson masses of 100–150  GeV/c2 using data from run II at the Fermilab Tevatron. For mH=120  GeV/c2, we exclude cross sections larger than 38 times the standard-model prediction.