This paper presents the first measurement of the inclusive J/Psi production cross section in the forward pseudorapidity region 2.5<|eta|<3.7 in ppbar collisions at sqrt(s)=1.8TeV. The results are based on 9.8 pb-1 of data collected using the D0 detector at the Fermilab Tevatron Collider. The inclusive J/Psi cross section for transverse momenta between 1 and 16 GeV/c is compared with theoretical models of charmonium production.