Using the data collected with the D0 detector at square root(s) = 1.96 TeV, for integrated luminosities of about 180 pb(-1), we have measured the ratio of inclusive cross sections for pp --> Z + b jet to pp --> Z + jet production. The inclusive Z + b-jet reaction is an important background to searches for the Higgs boson in associated ZH production at the Fermilab Tevatron collider. Our measurement is the first of its kind, and relies on the Z --> e+ e- and Z --> mu+ mu- modes. The combined measurement of the ratio yields 0.021+/-0.005 for hadronic jets with transverse momenta pT > 20 GeV/c and pseudorapidities absolute value(eta) < 2.5, consistent with next-to-leading-order predictions of the standard model.