Zero-shot skeleton-based action recognition aims to recognize unseen actions by transferring knowledge from seen categories through semantic descriptions. Most existing methods typically align skeleton features with textual embeddings within a shared latent space. However, the absence of contextual cues, such as objects involved in the action, introduces an inherent gap between skeleton and semantic representations, making it difficult to distinguish visually similar actions. To address this, we propose SkeletonContext, a prompt-based framework that enriches skeletal motion representations with language-driven contextual semantics. Specifically, we introduce a Cross-Modal Context Prompt Module, which leverages a pretrained language model to reconstruct masked contextual prompts under guidance derived from LLMs. This design effectively transfers linguistic context to the skeleton encoder for instance-level semantic grounding and improved cross-modal alignment. In addition, a Key-Part Decoupling Module is incorporated to decouple motion-relevant joint features, ensuring robust action understanding even in the absence of explicit object interactions. Extensive experiments on multiple benchmarks demonstrate that SkeletonContext achieves state-of-the-art performance under both conventional and generalized zero-shot settings, validating its effectiveness in reasoning about context and distinguishing fine-grained, visually similar actions.