We report on a search for the pair production of scalar leptoquarks (LQ), using 191  pb−1 of proton-antiproton collision data recorded by the CDF experiment during Run II of the Tevatron. The leptoquarks are sought via their decay into a neutrino and quark yielding missing transverse energy and several jets of large transverse energy. No evidence for LQ production is observed, and limits are set on σ(pp→LQLQX→ννqqX). Using a next-to-leading order theoretical prediction of the cross section for LQ production, we exclude first-generation LQ in the mass interval 78 to 117  GeV/c2 at the 95% confidence level for BR(LQ→νq)=100%.