A measurement of the b jet production cross section is presented for events containing a Z boson produced in pp¯ collisions at s√=1.96  TeV, using data corresponding to an integrated luminosity of 2  fb−1 collected by the CDF II detector at the Tevatron. Z bosons are selected in the electron and muon decay modes. Jets are considered with transverse energy ET>20  GeV and pseudorapidity |η|<1.5 and are identified as b jets using a secondary vertex algorithm. The ratio of the integrated Z+b jet cross section to the inclusive Z production cross section is measured to be 3.32±0.53(stat)±0.42(syst)×10−3. This ratio is also measured differentially in jet ET, jet η, Z-boson transverse momentum, number of jets, and number of b jets. The predictions from leading-order Monte Carlo generators and next-to-leading-order QCD calculations are found to be consistent with the measurements within experimental and theoretical uncertainties.