  This paper shows that, a quasi-localization of wavefunctions in toroidal
compactifications with magnetic fluxes can lead to a strong suppression for
relevant Yukawa couplings, and it is applicable to obtain tiny neutrino masses.
Although it is known that magnetic fluxes lead to a Gaussian profile of
zero-modes on a torus and that can yield a suppressed coupling in
higher-dimensional supersymmetric Yang-Mills (SYM) theories, the largest
(diagonal) entry of Yukawa matrices is always of $\mathcal O(1)$. In this
paper, we propose a way to induce an absolutely tiny global factor of Yukawa
matrices. In two SYM theories defined in different dimensional spacetime, their
bifundamental representations must be localized as a point in some directions.
Overlaps of such point-like localized wavefunctions and Gaussian zero-modes
give a global factor of Yukawa matrices, and it can be a strong suppression
factor or a usual $\mathcal O(1)$ factor, corresponding to their distance. Our
numerical analysis shows that it is possible to obtain a suppression strong
enough to realize the tiny neutrino masses without a hard fine-tuning.
Furthermore, we propose a concrete model of the tiny neutrino Yukawa couplings
in a magnetized SYM system.
