  Consequences of a specific class of two Higgs doublet models in which the
Higgs induced tree level flavour changing neutral currents (FCNC) display
minimal flavour violation (MFV) are considered. These FCNC are fixed in terms
of the CKM matrix elements and the down quark masses. The minimal model in this
category with only two Higgs doublets has no extra CP violating phases but such
a phase can be induced by adding a complex singlet. Many of the theoretical
predictions are similar to other MFV scenario. The FCNC contribute
significantly to $B$ meson mixing and CP violation. Detailed numerical analysis
to determine the allowed Higgs contributions to neutral meson mixings and the
CKM parameters $\bar{\rho},\bar{\eta}$ in their presence is presented. The
Higgs induced phase in the $B^0_{d,s}-\bar{B}^0_{d,s}$ transition amplitude
$M_{12}^{d,s}$ is predicted to be equal for the $B_d$ and the $B_s$ systems.
There is a strong correlation between phases in $M_{12}^{d,s}$ and $|V_{ub}|$.
A measurable CP violating phase $\phi_s=-0.18\pm 0.08$ is predicted on the
basis of the observed phase $\phi_d$ in the $B_d$ system if $|V_{ub}|$ is large
and close to its value determined from the inclusive b decays.
