We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H is an element of (1/2, 1) and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint mean-field backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumptions, which generalize the classical ones, the necessary condition for the optimality of an admissible control is also sufficient.