We establish an Extreme Value Theory for a class of systems of diffusive particles with mean-field interaction in the drifts. First, we show that as the number of particles grows large, a point process that captures the upper order statistics of the system has the same limit as when the particles are replaced by independent copies of solution to the corresponding McKean-Vlasov SDE (propagation of chaos). Then, we employ tools from standard Extreme Value Theory along with Malliavin Calculus to characterize the limit. We deduce that under certain growth conditions, the normalized top-ranked particle will acquire a Gumbel law in the large-population limit.