We report on a search for the standard-model Higgs boson in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using an integrated luminosity of 2.0/fb. 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 $V(\to q\bar{q}/qq')H(\to b\bar{b})$ decay for Higgs boson masses of 100-150 GeV/$c^2$ using data from Run II at the Fermilab Tevatron. For $m_H=120$ GeV/$c^2$, we exclude cross sections larger than 38 times the standard-model prediction.

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