We report on a search for charge-1/3 third-generation leptoquarks (LQ) produced in ppbar collisions at sqrt(s)=1.96 TeV using the D0 detector at Fermilab. Third generation leptoquarks are assumed to be produced in pairs and to decay to a tau neutrino and a b quark with branching fraction B. We place upper limits on sigma(ppbar->LQLQbar)*B^2 as a function of the leptoquark mass M_{LQ}. Assuming B=1, we exclude at the 95% confidence level third-generation scalar leptoquarks with M_{LQ} < 229 GeV.