Events collected by the Collider Detector at Fermilab (CDF) with an energetic jet plus large missing transverse energy can be used to search for physics beyond the standard model. We see no deviations from the expected backgrounds and set upper limits on the production of new processes. We consider in addition the production of light gravitinos and set a limit at 95% confidence level on the breaking scale F−−√≥217GeV, which excludes gravitino masses smaller than 1.1×10−5eV/c2.