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Multi-view clustering (MVC) leverages complementary information from diverse data sources to enhance clustering performance. However, its practical deployment in distributed and privacy-sensitive scenarios remains challenging. Federated multi-view clustering (FMVC) has emerged as a potential solution, but existing approaches suffer from substantial limitations, including excessive communication overhead, insufficient privacy protection, and inadequate handling of missing views. To address these issues, we propose Efficient Federated Incomplete Multi-View Clustering (EFIMVC), a novel framework that introduces a localized optimization strategy to significantly reduce communication costs while ensuring theoretical convergence. EFIMVC employs both view-specific and shared anchor graphs as communication variables, thereby enhancing privacy by avoiding the transmission of sensitive embeddings. Moreover, EFIMVC seamlessly extends to scenarios with missing views, making it a practical and scalable solution for real-world applications. Extensive experiments on benchmark datasets demonstrate the superiority of EFIMVC in clustering accuracy, communication efficiency, and privacy preservation. Our code is publicly available at https://github.com/Tracesource/EFIMVC.