Online platforms such as Amazon and Netflix serve users across multiple countries and regions, underscoring the importance of multi-market recommendation (MMR). Most MMR methods adopt a pre-training and fine-tuning paradigm, in which a unified model is first trained on centralized, global data and subsequently adapted to specific markets. However, this approach ignores the privacy of market data. While traditional federated learning preserves privacy, it typically aims to obtain a global model by aggregating model parameters and does not account for significant market heterogeneity. Additionally, because ID spaces are disjoint across markets, embedding-based aggregation strategies become ineffective. To overcome these challenges, we propose a federated collaborative signal quantization (FedMM) method for multi-market click-through rate (CTR) prediction. Our core idea leverages a discrete codebook mechanism to achieve privacy-preserving transmission and align disjoint ID spaces. We further employ a hierarchical codebook structure to capture cross-market shared patterns and market-specific characteristics. Specifically, we deploy a residual quantized variational autoencoder (RQ-VAE) with a dual-layer codebook mechanism for each market to quantize collaborative embeddings. The first layer utilizes a global federated codebook, updated via aggregation to capture universally shared collaborative patterns, while the second layer maintains a local codebook to learn market-specific semantics. Finally, the learned discrete codes, which integrate both general and specific collaborative signals, are incorporated into downstream CTR models to enhance prediction accuracy across all markets. Extensive experiments on benchmark datasets demonstrate that FedMM significantly improves recommendation performance with privacy guarantees.