  First-principles lattice determinations of the Standard Model expectation for
the leading order hadronic vacuum polarization contribution to the anomalous
magnetic moment of the muon have become sufficiently precise that further
improvement requires including strong and electromagnetic isospin-breaking
effects. We provide a continuum estimate of the strong isospin-breaking
contribution, $a_\mu^{SIB}$, using $SU(3)$ chiral perturbation theory. The
result is shown to be dominated by resonance-region contributions encoded in a
single low-energy constant whose value is known from flavor-breaking hadronic
$\tau$ decay sum rules. Implications of the form of the result for lattice
determinations of $a_\mu^{SIB}$ are also discussed.
