Healthcare systems face an unprecedented surge in sophisticated cyberattacks, with ransomware, data breaches, and advanced persistent threats (APTs) posing severe risks to patient safety and data privacy. Traditional security information and event management (SIEM) systems struggle to keep pace with the evolving threat landscape, demonstrating detection rates below 75% for novel attacks and generating excessive false positives that overwhelm security operations centers. This paper presents a comprehensive AI-driven cybersecurity framework specifically designed for healthcare environments. Our approach integrates multiple machine learning algorithms including Isolation Forest for anomaly detection, Long Short-Term Memory (LSTM) networks for temporal pattern recognition, and ensemble methods combining Random Forest, Convolutional Neural Networks (CNN), and Deep Neural Networks (DNN) to achieve superior threat detection and automated response capabilities. Through extensive evaluation across simulated and real-world healthcare network environments, our ensemble model achieved 98.5% accuracy in threat detection, with precision of 98.2%, recall of 97.9%, and an F1-score of 98.0%. The false positive rate was reduced to 1.8%, compared to 12.5% for traditional SIEM systems. Average threat detection time improved from 45-240 minutes (traditional methods) to 1.8-5.2 minutes (AI-enhanced system), enabling rapid response to critical threats. The framework incorporates automated response mechanisms, continuous learning capabilities, and HIPAA-compliant data handling procedures, making it practical for deployment in resource-constrained healthcare environments. Implementation costs range from $400K-$800K, with projected ROI of 220-340% within 24 months through reduced breach incidents, minimized downtime, and lower operational overhead.