The characterization of self-diffusion in MgO grain boundaries is a materials science problem of general interest, being relevant to the stability and reactivity of MgO layers in artificial nanostructures as well as to the understanding of mass transport and morphological evolution in polycrystalline metal oxides which are employed in many technological applications. In addition, atomic transport in MgO is a key factor to describe the rheology of the Earth's lower mantle. In this work, we tackle the problem using a classical molecular dynamics model and finite-temperature simulations. To this purpose, we first design a stable grain boundary structure, which is meant to be representative of general internal interfaces in nanocrystalline MgO. The Mg and O self-diffusion coefficients along this grain boundary are then determined as a function of temperature by calculating the mean-square ionic displacement in the boundary region. Two different diffusion regimes at low and high temperature are identified, allowing to obtain the relevant activation enthalpies for migration from the temperature dependance of the diffusion coefficients. Our results prove that Mg diffusion along MgO grain boundaries is sufficiently fast to explain the recently reported development of MgO hollow structures during repeated hydrogen sorption cycles in Mg/MgO nanoparticles.