The inclusive dijet production double differential cross section as a function of the dijet invariant mass and of the largest absolute rapidity of the two jets with the largest transverse momentum in an event is measured in proton anti-proton collisions at sqrt{s} = 1.96 TeV using 0.7 fb^{-1} integrated luminosity collected with the D0 detector at the Fermilab Tevatron Collider. The measurement is performed in six rapidity regions up to a maximum rapidity of 2.4. Next-to-leading order perturbative QCD predictions are found to be in agreement with the data.