We report a measurement of the forward-backward asymmetry, $A_{FB}$, in
$bar{b}$ 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 $A_{FB}(bar{b})=(1.2 pm 0.7)$\% at the particle level for
$b$-quark pairs with invariant mass, $m_{bar{b}}$, down to $40$ GeV/$c^2$ and
measure the dependence of $A_{FB}(bar{b})$ on $m_{bar{b}}$. The results are
compatible with expectations from the standard model.
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