Large Language Models (LLMs) are increasingly embedded in enterprise workflows, yet their performance remains highly sensitive to prompt design. Automatic Prompt Optimization (APO) seeks to mitigate this instability, but existing approaches face two persistent challenges. First, commonly used prompt strategies rely on static instructions that perform well on average but fail to adapt to heterogeneous queries. Second, more dynamic approaches depend on offline reward models that are fundamentally correlational, confounding prompt effectiveness with query characteristics. We propose Causal Prompt Optimization (CPO), a framework that reframes prompt design as a problem of causal estimation. CPO operates in two stages. First, it learns an offline causal reward model by applying Double Machine Learning (DML) to semantic embeddings of prompts and queries, isolating the causal effect of prompt variations from confounding query attributes. Second, it utilizes this unbiased reward signal to guide a resource-efficient search for query-specific prompts without relying on costly online evaluation. We evaluate CPO across benchmarks in mathematical reasoning, visualization, and data analytics. CPO consistently outperforms human-engineered prompts and state-of-the-art automated optimizers. The gains are driven primarily by improved robustness on hard queries, where existing methods tend to deteriorate. Beyond performance, CPO fundamentally reshapes the economics of prompt optimization: by shifting evaluation from real-time model execution to an offline causal model, it enables high-precision, per-query customization at a fraction of the inference cost required by online methods. Together, these results establish causal inference as a scalable foundation for reliable and cost-efficient prompt optimization in enterprise LLM deployments.