The increasing adoption of cyber-physical microgrids introduces vulnerabilities to cyber threats, necessitating anomaly-aware control for secure operation. This study proposes a hybrid AI-driven cyber defense framework using Long Short-Term Memory (LSTM) networks and Autoencoders for real-time anomaly detection and mitigation. Implemented in an OpenDSS-based IEEE 13-node test feeder with TCP/IP-based SCADA control, the model integrates dynamic load variations and solar irradiance with cloud coverage effects. Cyber-attacks are introduced at 150 timesteps, disrupting system stability, and mitigated at 250 timesteps via an AI-enhanced resilient controller. Performance is assessed based on phase angle deviation, state-of-charge (SoC) variations, and voltage stability. Results demonstrate effective cyber threat mitigation, maintaining operational resilience with minimal performance degradation. The proposed AI-driven control mechanism provides an adaptive security solution for modern microgrids, enabling real-time response to adversarial intrusions.