We present the first measurement of dijet angular distributions in ppbar collisions at sqrt{s}=1.96TeV at the Fermilab Tevatron Collider. The measurement is based on a dataset corresponding to an integrated luminosity of up to 0.7fb-1 collected with the D0 detector. Dijet angular distributions have been measured over a range of dijet masses, from 0.25TeV to above 1.1TeV. The data are in good agreement with the predictions of perturbative QCD and are used to constrain new physics models including quark compositeness, large extra dimensions, and TeV-1 scale extra dimensions. For all models we set the most stringent direct limits to date.