The rapid digitalization of healthcare has unlocked unprecedented opportunities for efficiency, accessibility, and innovation, yet it has simultaneously introduced complex vulnerabilities that threaten the confidentiality, integrity, and availability of sensitive patient information. Healthcare information infrastructures, which integrate electronic health records, telemedicine platforms, and connected medical devices, are increasingly targeted by cybercriminals seeking to exploit systemic weaknesses. Traditional security approaches, largely reliant on static defenses, are proving inadequate against evolving attack vectors such as ransomware, advanced persistent threats, and insider risks. This context underscores the urgent need for dynamic, intelligence-driven approaches to protect healthcare systems. Predictive analytics and machine learning have emerged as powerful tools capable of shifting cybersecurity from reactive to proactive. By leveraging vast datasets from network logs, medical devices, and patient management systems, predictive models can identify subtle anomalies and forecast potential threats before they fully materialize. Machine learning algorithms, particularly deep learning and ensemble techniques, enhance detection accuracy by continuously adapting to new patterns, reducing false positives, and enabling automated response mechanisms. Beyond detection, these models contribute to threat mitigation by prioritizing risks and supporting real-time decision-making for incident response teams. This paper advances the discourse by examining how predictive analytics and machine learning can be operationalized within healthcare settings to detect, mitigate, and prevent cyber threats. Special attention is given to scalability challenges, regulatory compliance, and ethical concerns surrounding patient data privacy. Ultimately, integrating predictive models with robust governance frameworks offers a pathway toward resilient healthcare infrastructures capable of sustaining trust, safeguarding sensitive data, and ensuring continuity of care.