Nonparametric estimation of nonlocal interaction kernels arises in a variety of applications using systems of interacting particles. The inference problem is at the intersection of statistic learning and inverse problems. Due to the nonlocal dependency, an open question is if its optimal minimax rate of convergence is the same as the classical nonparametric regression, that is, $M^{-\frac{2\beta}{2\beta+1}}$, in samples size $M$ and Holder exponent $\beta$ of the radial interaction kernel. This study provides an affirmative answer for systems with a finite number of particles. A key innovation is a tamed least square estimator (tLSE) that achieves a convergence rate matching the lower bound minimax rate for a large class of distributions. The tLSE comes along with a uniform low tail probability of the smallest eigenvalue of the normal matrix for all dimensions of the hypothesis spaces. The lower bound is obtained by overcoming the difficulty of nonlocal dependence via the hypothesis testing method.