This paper considers an $n$-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $n\to\infty$ of the empirical measure of the jump-diffusions to the solution of a deterministic McKean-Vlasov equation. The strong well-posedness of the associated McKean-Vlasov equation and a corresponding propagation of chaos result are proven. In particular, we provide also precise estimates of the convergence speed with respect to a Wasserstein-like metric.