Molecular Dynamics simulations were performed for the prediction of the finite-size effects of Maxwell-Stefan diffusion coefficients of molecular mixtures and a wide variety of binary Lennard-Jones systems. A strong dependency of computed diffusivities on the system size was observed. Computed diffusivities were found to increase with the number of molecules. We propose a correction for the extrapolation of Maxwell-Stefan diffusion coefficients to the thermodynamic limit, based on the study by Yeh and Hummer (J. Phys. Chem. B, 2004, 108, 15873-15879). The proposed correction is a function of the viscosity of the system, the size of the simulation box, and the thermodynamic factor, which is a measure for the nonideality of the mixture. Verification is carried out for more than 200 distinct binary Lennard-Jones systems, as well as 9 binary systems of methanol, water, ethanol, acetone, methylamine, and carbon tetrachloride. Significant deviations between finite-size Maxwell-Stefan diffusivities and the corresponding diffusivities at the thermodynamic limit were found for mixtures close to demixing. In these cases, the finite-size correction can be even larger than the simulated (finite-size) Maxwell-Stefan diffusivity. Our results show that considering these finite-size effects is crucial and that the suggested correction allows for reliable computations.