We present measurements of the inclusive production cross sections of the Upsilon(1S) bottomonium state in ppbar collisions at sqrt(s) = 1.96 TeV. Using the Upsilon(1S) to mu+mu- decay mode for a data sample of 159 +- 10 pb^-1 collected by the D0 detector at the Fermilab Tevatron collider, we determine the differential cross sections as a function of the Upsilon(1S) transverse momentum for three ranges of the Upsilon(1S) rapidity: 0 < |y| < 0.6, 0.6 < |y| < 1.2, and 1.2 < |y| < 1.8.