  We establish a correspondence between those Feynman diagrams in the MSSM
which give supersymmetric contributions to the muon anomalous magnetic moment
and those which contribute to the flavor violating processes $\mu --> e\gamma$
and $\tau --> \mu\gamma$. Using current experimental limits on the branching
ratios of these decay modes, combined with the assumption of a supersymmetric
contribution to the muon anomalous magnetic moment, we establish bounds on the
size of the lepton flavor violating soft masses in the MSSM largely independent
of assumptions about other supersymmetric parameters. If the deviation measured
at Brookhaven National Laboratory is from supersymmetry, we find the bounds
${m^2}_{e \mu}/ {{\bar{m}}^2} \lsim 2 \times 10^{-4}$ and ${m^2}_{\tau \mu}/
{{\bar{m}}^2} \lsim 1 \times 10^{-1}$, where ${\bar{m}}^2$ is the mass of the
heaviest particle in any loop that contributes at this level to the anomalous
magnetic moment of the muon. This provides a significant constraint on the
non-flavor-blind mediation of supersymmetry breaking that often occurs at a
suppressed level in many models, including gaugino mediation.
