Biodegradable self-healing hydrogels are attractive materials for tissue repair; however, the impact of the self-healing abilities of hydrogels on tissue repair is not clear. In this study, we prepared novel chitosan–cellulose nanofiber (CS–CNF) composite self-healing hydrogels with the same modulus (approximately 2 kPa) but tunable self-healing properties. By adding a low amount of CNFs (0.06–0.15 wt%) in the pristine chitosan (CS) self-healing hydrogel, the reversible dynamic Schiff bonding, strain sensitivity, and self-healing of the hydrogel are obviously affected. Neural stem cells embedded in the CS–CNF hydrogel with better self-healing properties reveal significantly enhanced oxygen metabolism as well as neural differentiation. The differentiation of neural stem cells is highly correlated with their metabolic change in the self-healing hydrogel. Moreover, the neural regeneration effect of the optimized CS–CNF hydrogel with 0.09 wt% CNFs and the best self-healing properties show a 50% improvement over the pristine CS hydrogel in the zebrafish brain injury model. A mechanism is proposed to interpret the tunable self-healing properties of CS–CNF hydrogels with stiffness maintained in a similar range. The new self-healing hydrogels help to clarify the role of self-healing in the biological performance of hydrogels as well as provide design rationale for hydrogels with better injectability and tissue regeneration potential.