  We study Majorana neutrino masses induced by D-brane instanton effects in
magnetized orbifold models. We classify possible cases, where neutrino masses
can be induced. Three and four generations are favored in order to generate
neutrino masses by D-brane instantons. Explicit mass matrices have specific
features. Their diagonalizing matrices correspond to the bimaximal mixing
matrix in the case with even magnetic fluxes, independently of the modulus
value $\tau$. On the other hand, for odd magnetic fluxes, diagonalizing
matrices correspond nearly to the tri-bimaximal mixing matrix near $\tau =i$,
while they become the bimaximal mixing matrix for larger ${\rm Im}\tau$. For
even fluxes, neutrino masses are modular forms of the weight 1 on
$T^2/\mathbb{Z}_2$, and they have symmetries such as $S_4'$ and
${\Delta'}(96)\times \mathbb{Z}_3$.
