© 2016 American Physical Society. We report a measurement of the forward-backward asymmetry, AFB, in bb pairs produced in proton-antiproton collisions and identified by muons from semileptonic b-hadron decays. The event sample is collected at a center-of-mass energy of s=1.96 TeV with the CDF II detector and corresponds to 6.9 fb-1 of integrated luminosity. We obtain an integrated asymmetry of AFB(bb)=(1.2±0.7)% at the particle level for b-quark pairs with invariant mass, mbb, down to 40 GeV/c2 and measure the dependence of AFB(bb) on mbb. The results are compatible with expectations from the standard model.