In this paper, we consider the matroid bandit optimization problem, a fundamental and widely applicable framework for combinatorial multi-armed bandits where the action space is constrained by a matroid. We tackle the challenge of devising algorithms that can cope with adversarial contamination of the feedback rewards, which may severely degrade the performance or even mislead existing methods. Our main contribution is an efficient and robust algorithm, dubbed ROMM, which builds upon the idea of optimistic matroid maximization and leverages robust statistical techniques to estimate the quality of the base arms in polynomial time. We establish lower bounds for matroid bandit optimization under the \(\epsilon \) -contamination model we adopt and show that ROMM achieves near-optimal regret bounds up to polylogarithmic factors. Furthermore, our analysis unveils a sharp phase transition between the small contamination regime and the large contamination regime for matroid bandit optimization. We establish that our algorithm can tolerate up to a universal constant fraction of corrupted feedbacks, which is optimal under mild conditions.