The integration of Generative Artificial Intelligence (GenAI) in healthcare is impeded by significant security challenges unaddressed by traditional frameworks, precisely the data-in-use gap where sensitive patient data and proprietary AI models are exposed during active processing. To address this, the paper proposes the Confidential Zero-Trust Framework (CZF), a novel security paradigm that synergistically combines Zero-Trust Architecture for granular access control with the hardware-enforced data isolation of Confidential Computing. We detailed a multi-tiered architectural blueprint for implementing the CZF on Google Cloud and analyzed its efficacy against real-world threats. The CZF provides a defense-in-depth architecture where data remains encrypted while in-use within a hardware-based Trusted Execution Environment (TEE). The framework's use of remote attestation offers cryptographic proof of workload integrity, transforming compliance from a procedural exercise into a verifiable technical fact and enabling secure, multi-party collaborations previously blocked by security and intellectual property concerns. By closing the data-in-use gap and enforcing Zero-Trust principles, the CZF provides a robust and verifiable framework that establishes the necessary foundation of trust to enable the responsible adoption of transformative AI technologies in healthcare.