  We study the Higgs-boson mass spectrum of the minimal supersymmetric standard
model, in which the tree-level CP invariance of the Higgs potential is broken
explicitly by loop effects of soft-CP-violating Yukawa interactions related to
scalar quarks of the third generation. The analysis is performed by considering
the CP-non-invariant renormalization-group improved effective potential through
next-to-leading order that includes leading logarithms due to two-loop Yukawa
and QCD corrections. We find that the three neutral Higgs particles predicted
by the theory may strongly mix with one another, thereby significantly
modifying their tree-level couplings to fermions and to the $W^\pm$ and Z
bosons. We analyze the phenomenological consequences of such a minimal
supersymmetric scenario of explicit CP violation on the production rates of the
lightest Higgs particle, and discuss strategies for its potential discovery at
high-energy colliders.
