In this paper, an all-optical plasmonic switch based on a metal–insulator–metal (MIM) structure is proposed and numerically investigated. The proposed configuration consists of two MIM waveguides and a pair of asymmetric disks filled with a nonlinear Au/SiO₂ material, in which square-shaped gold nanostructures are embedded inside each disk. To achieve fast and low-power switching performance, both the Kerr nonlinearity of the dielectric material and the intrinsic optical nonlinearity of the gold nanostructures are simultaneously exploited. Finite-difference time-domain (FDTD) simulation results indicate that, at low input intensity, the structure exhibits a resonance at a wavelength of 840 nm. As the input optical intensity increases, the resonance wavelength undergoes a red shift due to the combined nonlinear effects, resulting in a sudden enhancement of the transmitted power. The switching threshold power is found to be approximately 0.08 mW/μm², while the maximum transmission reaches about 0.65. Owing to its compact size, low threshold power, and ultrafast response, the proposed plasmonic switch is a promising candidate for applications in plasmonic integrated circuits.