The Higgs sector of the minimal S(3)-invariant extension of the Standard Model with a Higgs sector including CP violation is analyzed. Three SU(2) doublets Higgs fields with complex vev's provide an interesting scenario to analyze the Higgs masses spectrum, trilinear self-couplings and CP violation. We present how the spontaneous electroweak symmetry breaking coming from three $S(3)$ Higgs fields gives interesting scenarios. When spontaneous CP violation arises from the Higgs field $S(3)$ singlet $H_S$ we get nine physical Higgs and three Goldstone bosons. On the other scenarios when spontaneous CP violation arises from the Higgs field $S(3)$ doublet $H_D$ we get eight physical Higgs and four Goldstone bosons. From the numerical analysis of the Higgs masses and trilinear self-couplings we find a physical solution for the scenario in which spontaneous CPB is provided by the single field $H_S$ for this scenario the scalar Higgs $H_4^0$ is identified whose mass is 125 GeV in good agreement with the latest experimental results and $\lambda_{H_{4}^0 H_{4}^0 H_{4}^0} \sim \lambda_{h^0 h^0 h^0}^{SM}$.