We perform a detailed conformal field theory analysis of D2-brane instanton effects in four-dimensional type IIA string vacua with intersecting D6-branes. In particular, we explicitly compute instanton induced fermion two-point couplings which play the role of perturbatively forbidden Majorana mass terms for right-handed neutrinos or MSSM μ terms. These results can readily be extended to higherdimensional operators. In concrete realizations of such nonperturbative effects, the Euclidean D2-branehas to wrap a rigid, supersymmetric cycle with strong constraints on the zero-mode structure. Their implications for type IIA compactifications on the T6/ (Z2 X Z2) orientifold with discrete torsion are analyzed. We also construct a local supersymmetric GUT-like model allowing for a class of Euclidean D2-branes whose fermionic zero modes meet all the constraints for generating Majorana masses in the phenomenologically allowed regime. Together with perturbatively realized Dirac masses, these nonperturbative couplings give rise to the seesaw mechanism.