We present the results of a search for leptoquark (LQ) pairs in (85.2 +- 3.7) pb^{-1} of p anti-p collider data collected by the D0 experiment at the Fermilab Tevatron. We observe no evidence for leptoquark production and set a limit on sigma(p anti-p -> LQ anti-LQ -> neutrino neutrino + jets) as a function of the mass of the leptoquark (m_{LQ}). Assuming the decay LQ -> neutrino q, we exclude scalar leptoquarks for m_{LQ} < 98 GeV/c^2, and vector leptoquarks for m_{LQ} < 200 GeV/c^2 and coupling which produces the minimum cross section, at a 95% confidence level
