We developed a novel method for measuring the dynamic surface tension of liquids using mechanically vibrated sessile droplets. Under continuous mechanical vibration, the shape of the deformed droplet was fitted by numerical analysis, taking into account the force balance at the drop surface and the momentum equation. The surface tension was determined by optimizing four parameters: the surface tension, the droplet's height, the radius of the droplet-substrate contact area, and the horizontal symmetrical position of the droplet. The accuracy and repeatability of the proposed method were confirmed using drops of distilled water as well as viscous aqueous glycerol solutions. The vibration frequency had no influence on surface tension in the case of pure liquids. However, for water-soluble surfactant solutions, the dynamic surface tension gradually increased with vibration frequency, which was particularly notable for low surfactant concentrations slightly below the critical micelle concentration. This frequency dependence resulted from the competition of two mechanisms at the drop surface: local surface deformation and surfactant transport towards the newly generated surface.