This paper establishes interior Morrey regularity for stable solutions of the $p$-Laplace equation $-{\mathrm{\Delta }}_{p}u=h(u)$ in $B_1\subset {\mathbb{R}}^d$, where $h$ belongs to $C^1(\mathbb{R})$. The results cover the endpoint case left unresolved by Cabré et al. Moreover, for positive nonlinearities $h$, a global Morrey estimate was obtained for stable solutions of a Dirichlet problem on any smooth, bounded, strictly convex domain.