Privacy-preserving federated learning allows multiple users to jointly train a model with coordination of a central server. The server only learns the final aggregation result, thereby preventing leakage of the users' (private) training data from the individual model updates. However, keeping the individual updates private allows malicious users to perform Byzantine attacks and degrade the model accuracy without being detected. Best existing defenses against Byzantine workers rely on robust rank-based statistics, e.g., the median, to find malicious updates. However, implementing privacy-preserving rank-based statistics is nontrivial and unscalable in the secure domain, as it requires sorting of all individual updates. We establish the first private robustness check that uses high break point rank-based statistics on aggregated model updates. By exploiting randomized clustering, we significantly improve the scalability of our defense without compromising privacy. We leverage the derived statistical bounds in zero-knowledge proofs to detect and remove malicious updates without revealing the private user updates. Our novel framework, zPROBE, enables Byzantine resilient and secure federated learning. Empirical evaluations demonstrate that zPROBE provides a low overhead solution to defend against state-of-the-art Byzantine attacks while preserving privacy.