We measure the particle-level forward-backward production asymmetry in $\mathrm{b\bar{b}}$ pairs with masses (m$\mathrm{b\bar{b}}$) larger than 150 GeV/c2, using events with hadronic jets and employing jet charge to distinguish b from $\bar{b}$. The measurement uses 9.5 fb-1 of $\mathrm{p\bar{p}}$ collisions at a center-of-mass energy of 1.96 TeV recorded by the CDF II detector. The asymmetry as a function of m$\mathrm{b\bar{b}}$ is consistent with zero, as well as with the predictions of the standard model. The measurement disfavors a simple model including an axigluon with a mass of 200 GeV/c2, whereas a model containing a heavier 345 GeV/c2 axigluon is not excluded.