We have searched for direct pair production of scalar top and scalar bottom quarks in 88 pb-1 of pp collisions at sqrt[s]=1.8 TeV with the CDF detector. We looked for events with a pair of heavy flavor jets and missing energy, consistent with scalar top (bottom) quark decays to a charm (bottom) quark and a neutralino. The numbers of events that pass our selections show no significant deviation from standard model expectations. We compare our results to the next-to-leading order scalar quark production cross sections to exclude regions in scalar quark-neutralino mass parameter space.