Recently, the concept of skin effect has gained considerable attention in the context of non-Hermitian photonics. The experimental realization of Hatano–Nelson systems in optical coupled cavities has provided the opportunity to consider the effect of optical nonlinearity. In this work, we probe the interplay between Kerr nonlinearity and non-Hermiticity in a Hatano–Nelson lattice. In particular, we examine the relation between self-focusing and the skin effect under single-channel excitation. Moreover, we numerically identify skin soliton solutions, which exhibit power threshold and spatial asymmetry.