Low-dose computed tomography (LDCT) reduces radiation exposure but often degrades image quality, potentially compromising diagnostic accuracy. Existing deep learning-based denoising methods focus primarily on pixel-level mappings, overlooking the potential benefits of high-level semantic guidance. Recent advances in vision-language models (VLMs) suggest that language can serve as a powerful tool for capturing structured semantic information, offering new opportunities to improve LDCT reconstruction. In this paper, we introduce LangMamba, a Language-driven Mamba framework for LDCT denoising that leverages VLM-derived representations to enhance supervision from normal-dose CT (NDCT). LangMamba follows a two-stage learning strategy. First, we pre-train a Language-guided AutoEncoder (LangAE) that leverages frozen VLMs to map NDCT images into a semantic space enriched with anatomical information. Second, we synergize LangAE with two key components to guide LDCT denoising: Semantic-Enhanced Efficient Denoiser (SEED), which enhances NDCT-relevant local semantic while capturing global features with efficient Mamba mechanism, and Language-engaged Dual-space Alignment (LangDA) Loss, which ensures that denoised images align with NDCT in both perceptual and semantic spaces. Extensive experiments on two public datasets demonstrate that LangMamba outperforms conventional state-of-the-art methods, significantly improving detail preservation and visual fidelity. Remarkably, LangAE exhibits strong generalizability to unseen datasets, thereby reducing training costs. Furthermore, LangDA loss improves explainability by integrating language-guided insights into image reconstruction and offers a plug-and-play fashion. Our findings shed new light on the potential of language as a supervisory signal to advance LDCT denoising. The code is publicly available on https://github.com/hao1635/LangMamba.