Using the data collected with the D0 detector at =1.96 TeV, for integrated luminosities of about 180 pb-1, we have measured the ratio of inclusive cross sections for pZ+b jet to pZ+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 Ze+e- and Zµ+µ- modes. The combined measurement of the ratio yields 0.021±0.005 for hadronic jets with transverse momenta pT>20 GeV/c and pseudorapidities ||<2.5, consistent with next-to-leading-order predictions of the standard model.