We present measurements of the inclusive production cross sections of the $\ensuremath{\Upsilon}(1S)$ bottomonium state in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\mathrm{TeV}$. Using the $\ensuremath{\Upsilon}(1S)\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay mode for a data sample of $159\ifmmode\pm\else\textpm\fi{}10\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ collected by the D0 detector at the Fermilab Tevatron collider, we determine the differential cross sections as a function of the $\ensuremath{\Upsilon}(1S)$ transverse momentum for three ranges of the $\ensuremath{\Upsilon}(1S)$ rapidity: $0<|{y}^{\ensuremath{\Upsilon}}|\ensuremath{\le}0.6$, $0.6<|{y}^{\ensuremath{\Upsilon}}|\ensuremath{\le}1.2$, and $1.2<|{y}^{\ensuremath{\Upsilon}}|\ensuremath{\le}1.8$.