Enterprise cloud databases and enterprise resource planning systems have become core operational infrastructure for Saudi organisations that are digitising finance, procurement, logistics, human capital, healthcare, utilities, and public services. Their value depends not only on functional coverage, but also on continuous availability, trustworthy data, rapid incident handling, and compliance with national cyber and data requirements. This review examines how artificial intelligence can support predictive monitoring and controlled self-healing for enterprise databases and ERP platforms in Saudi Arabia. The study draws on recent literature published between 2020 and 2025 on cloud ERP, microservice architecture, autonomous databases, AIOps, anomaly detection, predictive maintenance, cybersecurity governance, and Saudi data regulation. The review argues that self-healing should not be treated as unchecked automation. In mission-critical ERP environments, it must be designed as a governed socio-technical capability that links telemetry pipelines, explainable AI models, root-cause reasoning, policy-aware remediation, human approval gates, and post-incident learning. The paper contributes a Saudi-oriented conceptual architecture and an adoption framework that align predictive operations with resilience, data protection, service continuity, and organisational readiness. It concludes that AI-driven self-healing is most valuable when introduced progressively, beginning with observability and prediction, then moving toward low-risk automated remediation, database tuning, failover optimisation, and evidence-based governance.