A nanoscale optical filter based on metal-insulator-metal waveguides and a Kerr-type nonlinear nanoslot resonator is introduced and numerically investigated by finite-difference time-domain simulations. It is demonstrated that the resonant wavelengths of the nanoslot resonator experience a red shift due to the intensity dependence of the Kerr nonlinear effect. The simulation results reveal that the resonant modes of the proposed filter can be tuned by properly adjusting the input signal intensity without changing the dimensions of the filter structure. The findings of this study are useful for highly integrated optical circuits, for which we have limitations on the dimensions of the filter structure. In addition, the results are suitable for design of integrated optical waveguides and resonators based on the plasmonic effect. A significant advantage of the proposed tunable filter is its ease of fabrication.