We search for the standard model Higgs boson produced in association with an electroweak vector boson in events with no identified charged leptons, large imbalance in transverse momentum, and two jets where at least one contains a secondary vertex consistent with the decay of b hadrons. We use ∼1  fb−1 integrated luminosity of pp collisions at s√=1.96  TeV recorded by the Collider Detector at Fermilab II experiment at the Tevatron. We find 268 (16) single (double) b-tagged candidate events, where 248±43 (14.4±2.7) are expected from standard model background processes. We observe no significant excess over the expected background and thus set 95% confidence level upper limits on the Higgs boson production cross section for several Higgs boson masses ranging from 110 to 140  GeV/c2. For a mass of 115  GeV/c2, the observed (expected) limit is 20.4 (14.2) times the standard model prediction.