The marriage of federated learning and recommender system (FedRec) has been widely used to address the growing data privacy concerns in personalized recommendation services. In FedRecs, users' attribute information and behavior data (i.e., user-item interaction data) are kept locally on their personal devices, therefore, it is considered a fairly secure approach to protect user privacy. As a result, the privacy issue of FedRecs is rarely explored. Unfortunately, several recent studies reveal that FedRecs are vulnerable to user attribute inference attacks, highlighting the privacy concerns of FedRecs. In this paper, we further investigate the privacy problem of user behavior data (i.e., user-item interactions) in FedRecs. Specifically, we perform the first systematic study on interaction-level membership inference attacks on FedRecs. An interaction-level membership inference attacker is first designed, and then the classical privacy protection mechanism, Local Differential Privacy (LDP), is adopted to defend against the membership inference attack. Unfortunately, the empirical analysis shows that LDP is not effective against such new attacks unless the recommendation performance is largely compromised. To mitigate the interaction-level membership attack threats, we design a simple yet effective defense method to significantly reduce the attacker's inference accuracy without losing recommendation performance. Extensive experiments are conducted with two widely used FedRecs (Fed-NCF and Fed-LightGCN) on three real-world recommendation datasets (MovieLens-100K, Steam-200K, and Amazon Cell Phone), and the experimental results show the effectiveness of our solutions.