We report on a search for direct Kaluza-Klein graviton production in a data sample of 84   pb−1 of pp¯ collisions at s√=1.8  TeV, recorded by the Collider Detector at Fermilab. We investigate the final state of large missing transverse energy and one or two high energy jets. We compare the data with the predictions from a (3+1+n)-dimensional Kaluza-Klein scenario in which gravity becomes strong at the TeV scale. At 95% confidence level (C.L.) for n=2, 4, and 6 we exclude an effective Planck scale below 1.0, 0.77, and 0.71 TeV, respectively.