Certain string-inspired Z' models have non-universal interactions to three families of fermions and induced tree-level flavor-changing couplings. We use recent results on B_s-anti-B_s mixing to constrain the size of the flavor-changing couplings in the b-s sector. In some highly predictive Z' models, such a constraint on b-s coupling can be translated into the flavor-diagonal couplings. Based on the Z' production limits at the Tevatron, we obtain the limit on the leptonic couplings of Z' and

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... n make predictions for B_s -> μ^+ μ^- branching ratios. We conclude that with the present constraints from B_s mixing and Z' production, the muonic decay of B_s may not be observed at the Tevatron if the projected integrated luminosity is less than O(5-10) fb.