We report a measurement of the forward-backward asymmetry, AFB, in bb pairs produced in protonantiproton 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, m bb , down to 40 GeV/c 2 and measure the dependence of AFB(bb) on m bb . The results are compatible with expectations from the standard model.