We discuss the origin and phenomenological consequences of the flavour violating couplings of the neutral Higgs bosons to the down-type quarks generated in the minimal supersymmetric standard model (MSSM) for large values of  tan \beta . We concentrate on the scenario with minimal flavour and CP violation (MFV) and demonstrate the tight correlation of the B⁰_s-\bar B⁰_s mass difference with BR(B⁰_s\rightarrow \mu ⁺\mu ^-) and BR(B⁰_d\rightarrow \mu ⁺\mu ^-). While the first correlation holds also in the case of non-minimal flavour violation, the second one is specific for the minimal case and can potentially serve as a test of the sources of flavour violation in supersymmetry.

PACS numbers: 11.30.Hv, 12.15.Ji, 12.15.Mm, 12.60.Jv