  We consider magnetized orbifolds, where the supersymmetric mass term for a
pair of up- and down-type Higgs (super)fields, called $\mu$-term, is localized
at the orbifold fixed points, and study the effects on the zero-mode spectra.
The zero-mode degeneracy to be identified as the generation in four-dimensional
(4D) effective theories is determined by the magnetic fluxes. It is known that
multiple Higgs zero-modes appear in general in magnetized orbifold models. We
derive the analytic form of the $\mu$-term matrix in the 4D effective theory
generated by the localized sources on $T^2/Z_2$ orbifold fixed points, and find
that this matrix can lead to a distinctive pattern of the eigenvalues that
yields hierarchical $\mu$-terms for the multiple Higgs fields. The lightest
ones can be exponentially suppressed due to the localized wavefunctions of
zero-modes determined by the fluxes, while the others are of the order of the
compactification scale, which can provide a dynamical origin of the electroweak
scale as well as a simultaneous decoupling of extra Higgs fields. We also show
that a certain linear combination of the lightest Higgs fields could generate
the observed mass ratios of down-type quarks through their Yukawa couplings
determined by the wavefunctions.
