Inclusive jet cross sections in Z/γ∗ events, with Z/γ∗ decaying into an electron-positron pair, are measured as a function of jet transverse momentum and jet multiplicity in pp collisions at s√=1.96   TeV with the upgraded Collider Detector at Fermilab in run II, based on an integrated luminosity of 1.7   fb−1. The measurements cover the rapidity region |yjet|<2.1 and the transverse momentum range pjetT>30  GeV/c. Next-to-leading order perturbative QCD predictions are in good agreement with the measured cross sections.