<p>The increasing reliance on automatic code generation integrated with Generative AI technology has raised new challenges for cybersecurity defense against code injection, insecure code templates, and adversarial manipulation of an AI model. These risks make developing advanced frameworks imperative to ensure secure, reliable, and privacy-preserving code generation processes. The paper presents a novel Hybrid Artificial Neural Network (ANN)-Interpretive Structural Modeling (ISM) Framework to alleviate the cybersecurity risks associated with the automatic code generation using Generative AI. The proposed framework integrates the predictive capability of ANN and structured analysis of ISM for the identification, evaluation, and treatment of common vulnerabilities and risks in automatic code generation. We first conduct a multivocal literature review (MLR) to identify cybersecurity risks and generative AI practices for addressing these risks in automatic code generation. Then we conduct a questionnaire survey to identify and validate the identified risks and practices. An expert panel review was then assigned for the process of ANN-ISM. The ANN model can predict potential security risks by learning from historical data and code generation patterns. ISM is used to (1) structure and visualize (2) relations between identified risks and mitigation approaches and (3) offer a combined, multi-layered risk management methodology. We then perform an in-depth examination of the framework with a case study of an AI-based code generation company. We further determine its practicality and usefulness in real-world settings. The case study results show that the framework efficiently handles the primary cybersecurity challenges, such as injection attacks, code quality, backdoors, and lack of input validation. The analysis characterizes the maturity of several mitigation practices and areas for improvement for security integration with automatic code generation functionality. Advanced risk mitigation is enabled in the framework across multiple process areas, where techniques such as static code analysis, automated penetration testing, and adversarial training hold much promise. The Hybrid ANN-ISM Mechanism is a stable and flexible solution for cybersecurity risk reduction in automatic code generation environments. The coupling of ANN and ISM, in terms of predictive analysis and structured risk management, respectively, contributes effectively towards the security of AI-based code generation tools. More research is required to improve the scalability, privacy preserving, and dynamic integration of the framework with cybersecurity threat intelligence.</p>