  It has recently been shown that F-theory based constructions provide a
potentially promising avenue for engineering GUT models which descend to the
MSSM. In this note we show that in the presence of background fluxes, these
models automatically achieve hierarchical Yukawa matrices in the quark and
lepton sectors. At leading order, the existence of a U(1) symmetry which is
related to phase rotations of the internal holomorphic coordinates at the brane
intersection point leads to rank one Yukawa matrices. Subleading corrections to
the internal wave functions from variations in the background fluxes generate
small violations of this U(1), leading to hierarchical Yukawa structures
reminiscent of the Froggatt-Nielsen mechanism. The expansion parameter for this
perturbation is in terms of alpha_(GUT)^(1/2). Moreover, we naturally obtain a
hierarchical CKM matrix with V_(12) ~ V_(21) ~ epsilon, V_(23) ~ V_(32) ~
epsilon^(2), V_(13) ~ V_(31) ~ epsilon^(3), where epsilon ~ alpha_(GUT)^(1/2),
in excellent agreement with observation.
