Materials with strong optical Kerr effects (OKEs) are crucial for a broad range of applications, such as all-optical data processing and quantum information. However, the underlying OKE mechanism is not clear in 2D materials. Here, we reveal key insights of the OKE associated with 2D excitons. An admirably succinct formalism is derived for predicting the spectra and the magnitude of the nonlinear refractive index (n2) of 2D materials. The predicted n2 spectra are consistent with reported experimental data and exhibit pronounced excitonic resonances, which is distinctively different from bulk semiconductors. The n2 value is predicted to be 3×10-10cm2/W for a 2D layered perovskite at low temperature as 7 K, which is four orders of magnitude larger than those of bulk semiconductors. The superior OKE induced by 2D excitons would give rise to a narrow refractive index-near-zero region for intense laser light. Furthermore, we demonstrate that the 2D layered perovskite should exhibit the best OKE efficiency (WFOM=1.02, TFOM=0.14) at 1550 nm, meeting the material requirements for all-optical switching. Our findings deepen the understanding of the OKE of 2D semiconducting materials and pave the way for highly efficient all-optical excitonic devices.