Network Function Virtualization (NFV) transforms traditional network infrastructures by replacing hardware components with software-based Virtual Network Functions (VNFs). While NFV improves flexibility, scalability, and cost efficiency, it also introduces significant cybersecurity challenges due to vulnerabilities in virtualization layers, orchestration tools, and multi-tenant environments. Conventional intrusion detection systems and classical machine learning (ML) models such as Support Vector Machines, Random Forests, and traditional neural networks often fail to cope with evolving threats, leading to high false positives, computational overhead, and limited effectiveness against zero-day attacks. To address these limitations, this paper proposes a Quantum-Inspired Machine Learning (QiML) framework specifically designed for anomaly detection in NFV-cloud security. The framework integrates multiple modules: Quantum-inspired Feature Encoding (QiFE) for compact data representation, a Quantum-inspired Evolutionary Algorithm (QiEA) for feature selection, Quantum-inspired Neural Networks (QiNN) for accurate anomaly detection, an Adaptive Quantum-Inspired Cybersecurity Strategy for real-time mitigation, and Quantum-inspired Explainable AI (QiXAI) for interpretability. Experimental evaluations using CIC-IDS2018, UNSW-NB15, and NFV-specific synthetic datasets demonstrate the superior performance of the proposed framework. The QiEA + QiNN model achieved an accuracy of 98.20%, precision of 97.70%, recall of 97.40%, and F1-score of 97.55% on CIC-IDS2018, outperforming classical ML baselines. Furthermore, the framework reduced feature dimensionality and training time, enhancing efficiency for real-world NFV-cloud deployments. Overall, the QiML framework demonstrates strong potential for advancing secure, adaptive, and interpretable anomaly detection in NFV-cloud environments.