In this work we show a theoretical study of the electronic and transport properties of superlattices formed by a periodic structure of vacancies (antidots) on graphene nanoribbons. The systems are described by a single-band tight-binding Hamiltonian and also by ab initio total energy density-functional theory calculations. The quantum conductance is determined within the Green's function formalism, calculated by real-space renormalization techniques. A series of well defined gap structures on the conductance as a function of the Fermi energy is observed. This strongly depends on the period of the vacancies on the nanoribbon and on the internal geometrical structure of the supercell. Controlling these parameters could be possible to modulate the electronic response of the systems.