We searched for scalar bottom quarks in 156  pb−1 of pp collisions at s√=1.96  TeV recorded by the Collider Detector at Fermilab II experiment at the Tevatron. Scalar bottom quarks can be produced from gluino decays in R-parity conserving models of supersymmetry when the mass of the gluino exceeds that of the scalar bottom quark. Then, a scalar bottom quark can decay into a bottom quark and a neutralino. To search for this scenario, we investigated events with large missing transverse energy and at least three jets, two or more of which were identified as containing a secondary vertex from the hadronization of b quarks. We found four candidate events, where 2.6±0.7 are expected from standard model processes, and placed 95% confidence level lower limits on gluino and scalar bottom quark masses of up to 280 and 240  GeV/c2, respectively.