Production of jets in association with a $Z/\gamma^*$ boson in proton--proton collisions at $\sqrt{s} = 7$ TeV with the ATLAS detector. The analysis includes the full 2010 data set, collected with a low rate of multiple proton--proton collisions in the accelerator, corresponding to an integrated luminosity of 36 pb$^{-1}$. Inclusive jet cross sections in $Z/\gamma^*$ events, with $Z/\gamma^*$ decaying into electron or muon pairs, are measured for jets with transverse momentum $p_T > 30$ GeV and jet rapidity $|y| < 4.4$.