High-index dielectric metasurfaces can support sharp optical resonances enabled by the physics of bound states in the continuum (BICs) often manifested in experiments as quasi-BIC resonances. They provide a way to enhance light–matter interaction at the subwavelength scale bringing novel opportunities for nonlinear nanophotonics. Strong narrow-band field enhancement in quasi-BIC metasurfaces leads to an extreme sensitivity to a change of the refractive index that may limit nonlinear functionalities for the pump intensities beyond the perturbative regime. Here we study ultrafast self-action effects observed in quasi-BIC silicon metasurfaces and demonstrate how they alter the power dependence of the third-harmonic generation efficiency. We study experimentally a transition from the subcubic to supercubic regimes for the generated third-harmonic power driven by a blue-shift of the quasi-BIC in the multiphoton absorption regime. Our results suggest a way to implement ultrafast nonlinear dynamics in high-index resonant dielectric metasurfaces for nonlinear meta-optics beyond the perturbative regime.