We measure the neutral D total forward cross section and the differential cross sections as functions of Feynman- x ( x F) and transverse momentum squared for 500 GeV/ c π −–nucleon interactions. The results are obtained from 88 990±460 reconstructed neutral D mesons from Fermilab experiment E791 using the decay channels D 0→ K − π + and D 0→ K − π + π − π + (and charge conjugates). We extract fit parameters from the differential cross sections and provide the first direct measurement of the turnover point in the x F distribution, 0.0131±0.0038. We measure an absolute D 0+ D 0 ( x F>0) cross section of 15.4 +1.8 −2.3 μbarn/nucleon (assuming a linear A dependence). The differential and total forward cross sections are compared to theoretical predictions and to results of previous experiments.