In this paper, we study both the existence and uniqueness of nonnegative solutions for the nonlocal $p$-Laplace equation with singular term

where $\unicode[STIX]{x1D6FA}\subset \mathbb{R}^{N}(N\geqslant 1)$ is a bounded domain with smooth boundary $\unicode[STIX]{x2202}\unicode[STIX]{x1D6FA}$, $h\in L^{1}(\unicode[STIX]{x1D6FA})$, $h>0$ almost everywhere in $\unicode[STIX]{x1D6FA}$, $k\in L^{\infty }(\unicode[STIX]{x1D6FA})$ is a non-negative function, $B:[0,+\infty )\rightarrow [m,+\infty )$ is continuous for some positive constant $m$, $p>1$, $0\leqslant q\leqslant p-1$, and $\unicode[STIX]{x1D6FE}>1$. A “compatibility condition” on the couple $(h(x),\unicode[STIX]{x1D6FE})$ will be given for the problem to admit at least one solution. To be a little more precise, it is shown that the problem admits at least one solution if and only if there exists a $u_{0}\in W_{0}^{1,p}(\unicode[STIX]{x1D6FA})$ such that $\int _{\unicode[STIX]{x1D6FA}}h(x)u_{0}^{1-\unicode[STIX]{x1D6FE}}\text{d}x<\infty$. When $k(x)\equiv 0$, the weak solution is unique.