  We analyze the Higgs sector of the minimal $S(3)$-invariant extension of the
Standard Model including CP violation arising from the spontaneous electroweak
symmetry breaking. This extended Higgs sector includes three SU(2) doublets
Higgs fields with complex vev's providing an interesting scenario to analyze
the Higgs masses spectrum, trilinear Higgs self-couplings and CP violation. We
present how the spontaneous electroweak symmetry breaking coming from three
$S(3)$ Higgs fields gives an interesting scenario with nine physical Higgs and
three Goldstone bosons when spontaneous CP violation arises from the Higgs
field $S(3)$ singlet $H_S$. Furthermore, a numerical analysis of the Higgs
masses and trilinear Higgs self-couplings is presented. Particularly, we find a
physical solution for the scenario in which spontaneous CPB is provided by
$H_S$. In this scheme, the scalar Higgs $H^0_1$ is identified, whose mass is
125 GeV and $\lambda_{H_{1}^0 H_{1}^0 H_{1}^0} \sim \lambda_{h^0 h^0
h^0}^{SM}$.
