LLM-powered agents often use prompt compression to reduce inference costs, but this introduces a new security risk. Compression modules, which are optimized for efficiency rather than safety, can be manipulated by adversarial inputs, causing semantic drift and altering LLM behavior. This work identifies prompt compression as a novel attack surface and presents CompressionAttack, the first framework to exploit it. CompressionAttack includes two strategies: HardCom, which uses discrete adversarial edits for hard compression, and SoftCom, which performs latent-space perturbations for soft compression. Experiments on multiple LLMs show up to an average ASR of 83% and 87% in two tasks, while remaining highly stealthy and transferable. Case studies in three practical scenarios confirm real-world impact, and current defenses prove ineffective, highlighting the need for stronger protections.