Using the data collected with the D0 detector at $\sqrt{s}=1.96\text{ }\mathrm{TeV}$, for integrated luminosities of about $180\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$, we have measured the ratio of inclusive cross sections for $p\overline{p}\ensuremath{\rightarrow}Z+b\text{ }\mathrm{\text{jet}}$ to $p\overline{p}\ensuremath{\rightarrow}Z+\mathrm{\text{jet}}$ production. The inclusive $Z+b\mathrm{\text{\ensuremath{-}}}\mathrm{\text{jet}}$ 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 $Z\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ and $Z\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ modes. The combined measurement of the ratio yields $0.021\ifmmode\pm\else\textpm\fi{}0.005$ for hadronic jets with transverse momenta ${p}_{T}>20\text{ }\text{ }\mathrm{GeV}/c$ and pseudorapidities $|\ensuremath{\eta}|<2.5$, consistent with next-to-leading-order predictions of the standard model.