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Yukawa fluids consist of particles that interact through a repulsive or attractive Yukawa potential. A surface tension arises at the walls of the container that encloses the fluid or at the interface between two coexisting phases. We calculate that surface tension on the level of mean-field theory, thereby either ignoring the particle size (ideal Yukawa fluid) or accounting for a non-vanishing particle size through a nonideal contribution to the free energy, exemplified either on the level of a lattice gas (lattice Yukawa fluid) or based on the Carnahan-Starling equation of state (Carnahan-Starling Yukawa fluid). Our mean-field results, which do not rely on assuming small gradients of the particle concentrations, become exact in the limit of large temperature and large screening length. They are calculated numerically in the general case and analytically in the two limits of small particle concentration and close to the critical point for a phase-separating system. For a sufficiently small particle concentration, our predicted surface tension is accurate whereas for a phase boundary, we expect good agreement with exact calculations in the limit of a large screening length and if the mean-field model employs the Carnahan-Starling equation of state.