  We investigate the effects of the spontaneous CP violation at finite
temperature in the Minimal Supersymmetric Standard Model on the baryogenesis at
the weak scale. After a brief discussion of the case in which the electroweak
phase transition is of the second order, we study in details the baryogenesis
scenario when the transition proceeds via bubble nucleation. We show that the
space-time dependent phase for the Higgs vacuum expectation values coming from
the spontaneous CP violation can give rise to a efficient generation of baryon
number inside the bubble walls if the superpotential parameters and the soft
supersymmetry breaking ones are complex. However we find that in order to get
the observed value for the baryon asymmetry of the universe the phases of such
parameters can be as small as $10^{-5}$, giving rise to an electron dipole
moment of the neutron well below the current experimental limit. Moreover a
light Higgs pseudoscalar is needed, and an upper bound on its mass is obtained.
