The inclusive cross section for J/ψ production times the branching ratio B(J/ψ⃗ μ+μ-) has been measured in the forward pseudorapidity region: B×dσ[p¯+p⃗ J/ψ(pT>10GeV/c,2.1<|η|<2.6)+X]/dη=192±9(stat)±29(syst)pb. The results are based on 74.1±5.2pb-1 of data collected by the CDF Collaboration at the Fermilab Tevatron Collider. The measurements extend earlier measurements of the D0 Collaboration to higher pJ/ψT. In the kinematic range where the experiments partially overlap, these data are in good agreement with previous measurements.