We report a measurement of the forward-backward asymmetry, $A_{FB}$, in $bbar{b}$ pairs produced in proton-antiproton collisions and identified by muons from semileptonic $b$-hadron decays. The event sample was collected at a center-of-mass energy of $sqrt{s}=1.96$ TeV with the CDF II detector and corresponds to 6.9 fb$^{-1}$ of integrated luminosity. We obtain an integrated asymmetry of $A_{FB}(bbar{b})=(1.2 pm 0.7)$% at the particle level for $b$-quark pairs with invariant mass, $m_{bbar{b}}$, down to $40$ GeV/$c^2$ and measure the dependence of $A_{FB}(bbar{b})$ on $m_{bbar{b}}$. The results are compatible with expectations from the standard model.
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