We search for direct pair production of supersymmetric top quarks and supersymmetric bottom quarks in proton-antiproton collisions at s√=1.96  TeV, using 295  pb−1 of data recorded by the Collider Detector at Fermilab (CDF II) experiment. The supersymmetric top (supersymmetric bottom) quarks are selected by reconstructing their decay into a charm (bottom) quark and a neutralino, which is assumed to be the lightest supersymmetric particle. The signature of such processes is two energetic heavy-flavor jets and missing transverse energy. The number of events that pass our selection for each search process is consistent with the expected standard model background. By comparing our results to the theoretical production cross sections of the supersymmetric top and supersymmetric bottom quarks in the minimal supersymmetric standard model, we exclude, at a 95% confidence level in the frame of that model, a supersymmetric top quark mass up to 132  GeV/c2 for a neutralino mass of 48  GeV/c2, and a supersymmetric bottom quark mass up to 193  GeV/c2 for a neutralino mass of 40  GeV/c2.