The rapid commercialization of large language models (LLMs) has intensified model theft and unauthorized redistribution, particularly as these models are distributed in quantized formats. Existing watermarking techniques fail to survive the aggressive quantization process or degrade model performance. We propose FreMark, a novel frequency-domain watermarking approach that uses the Discrete Cosine Transform (DCT) to embed imperceptible watermarks into quantized LLMs. FreMark operates by transforming weight matrices into the frequency domain, where watermark signals are strategically embedded in high-frequency components less sensitive to model functionality. The key innovation lies in our interval-constrained embedding mechanism, which ensures that watermarked parameters remain within quantization-invariant intervals, guaranteeing watermark persistence even after quantization. During the training process, FreMark periodically applies frequency domain perturbations to selected weight matrices while maintaining strict adherence to quantization boundaries through our proposed clipping algorithm. This strategy ensures both watermark robustness and minimal impact on model performance. Experimental results demonstrate that FreMark successfully embeds verifiable watermarks in quantized LLMs with negligible performance degradation, with only a slight drop in watermark extraction accuracy and minimal impact on model perplexity.