The growing reliance on artificial intelligence (AI) in customer support has significantly improved operational efficiency and user experience. However, traditional machine learning (ML) approaches, which require extensive local training on sensitive datasets, pose substantial privacy risks and compliance challenges with regulations like the General Data Protection Regulation (GDPR) and California Consumer Privacy Act (CCPA). Existing privacy-preserving techniques, such as anonymization, differential privacy, and federated learning, address some concerns but face limitations in utility, scalability, and complexity. This paper introduces the Privacy-Preserving Zero-Shot Learning (PP-ZSL) framework, a novel approach leveraging large language models (LLMs) in a zero-shot learning mode. Unlike conventional ML methods, PP-ZSL eliminates the need for local training on sensitive data by utilizing pre-trained LLMs to generate responses directly. The framework incorporates real-time data anonymization to redact or mask sensitive information, retrieval-augmented generation (RAG) for domain-specific query resolution, and robust post-processing to ensure compliance with regulatory standards. This combination reduces privacy risks, simplifies compliance, and enhances scalability and operational efficiency. Empirical analysis demonstrates that the PP-ZSL framework provides accurate, privacy-compliant responses while significantly lowering the costs and complexities of deploying AI-driven customer support systems. The study highlights potential applications across industries, including financial services, healthcare, e-commerce, legal support, telecommunications, and government services. By addressing the dual challenges of privacy and performance, this framework establishes a foundation for secure, efficient, and regulatory-compliant AI applications in customer interactions.