Self-diffusion coefficients of Yukawa systems in the fluid phase are obtained from molecular dynamics simulations in a wide range of the thermodynamical parameters. The Yukawa system is a collection of particles interacting through Yukawa (i.e., screened Coulomb) potentials, which may serve as a model for charged dust particles in a plasma or colloidal particles in electrolytes. The self-diffusion coefficients are found to follow a simple scaling law with respect to the system temperature, which is consistent with the universal scaling (i.e., temperature scaling independent of the ratio of interparticle distance to screening length) observed by Robbins et al. [J. Chem. Phys. 88, 3286 (1988)] if the fluid system is near solidification. Also discussed is the velocity autocorrelation function, which is in part used to determine the self-diffusion coefficients through the Green–Kubo formula.