  We analyse the rare decay mode B_s -> mu^+ mu^- in the minimal supergravity
scenario (mSUGRA). We find a strong correlation with the muon anomalous
magnetic moment (g-2)_mu. An interpretation of the recently measured excess in
(g-2)_mu in terms of mSUGRA corrections implies a substantial supersymmetric
enhancement of the branching ratio Br(B_s -> mu^+ mu^-): if (g-2)_mu exceeds
the Standard Model prediction by 4*10^{-9}, Br(B_s -> mu^+ mu^-) is larger by a
factor of 10-100 than in the Standard Model and within reach of Run-II of the
Tevatron. Thus an experimental search for B_s -> mu^+ mu^- is a stringent test
of the mSUGRA GUT scale boundary conditions. If the decay B_s -> mu^+ mu^- is
observed at Run-II of the Tevatron, then we predict the mass of the lightest
supersymmetric Higgs boson to be less than 120 GeV. The decay B_s -> mu^+ mu^-
can also significantly probe the favoured parameter range in SO(10) SUSY GUT
models.
