Prompt injection attacks have become an increasing vulnerability for LLM applications, where adversarial prompts exploit indirect input channels such as emails or user-generated content to circumvent alignment safeguards and induce harmful or unintended outputs. Despite advances in alignment, even state-of-the-art LLMs remain broadly vulnerable to adversarial prompts, underscoring the urgent need for robust, productive, and generalizable detection mechanisms beyond inefficient, model-specific patches. In this work, we propose Zero-Shot Embedding Drift Detection (ZEDD), a lightweight, low-engineering-overhead framework that identifies both direct and indirect prompt injection attempts by quantifying semantic shifts in embedding space between benign and suspect inputs. ZEDD operates without requiring access to model internals, prior knowledge of attack types, or task-specific retraining, enabling efficient zero-shot deployment across diverse LLM architectures. Our method uses adversarial-clean prompt pairs and measures embedding drift via cosine similarity to capture subtle adversarial manipulations inherent to real-world injection attacks. To ensure robust evaluation, we assemble and re-annotate the comprehensive LLMail-Inject dataset spanning five injection categories derived from publicly available sources. Extensive experiments demonstrate that embedding drift is a robust and transferable signal, outperforming traditional methods in detection accuracy and operational efficiency. With greater than 93% accuracy in classifying prompt injections across model architectures like Llama 3, Qwen 2, and Mistral and a false positive rate of <3%, our approach offers a lightweight, scalable defense layer that integrates into existing LLM pipelines, addressing a critical gap in securing LLM-powered systems to withstand adaptive adversarial threats.