In this work we develop an efficient numerical solution method for solving potential mean field games with multiple species. This is done by using recent developments that connect mean field games and entropy-regularized optimal transport. In particular, we reformulate the original problem as a structured entropy-regularized multi-marginal optimal transport problem, and develop highly efficient methods for solving the latter. Finally, we illustrate the proposed method on a problem with four interacting species, where each of the species has different target objectives.