Abstract: We extend the Dong-Mason theorem on irreducibility of modules for orbifold vertex algebras (cf. ) to the category of weak modules. Let V be a vertex operator algebra, g an automorphism of order p. Let W be an irreducible weak V–module such that are inequivalent irreducible modules. We prove that W is an irreducible weak –module. This result can be applied on irreducible modules of certain Lie algebra L such that are Whittaker modules having different Whittaker functions. We present certain applications in the cases of the Heisenberg and Weyl vertex operator algebras.