The expansion of generative artificial intelligence (GenAI) creates new opportunities for administrative efficiency, data analysis, communication, and decision support in educational institutions, while simultaneously raising concerns about privacy, bias, opacity, cognitive dependence, and blurred human accountability. This study develops a context-sensitive governance framework for GenAI in Islamic educational institutions. It employs an integrative literature review and thematic-comparative analysis of peer-reviewed scholarship on AI in educational leadership and management, responsible AI, AI literacy, digital transformation, and Islamic educational management. The synthesis produces the Amanah–Adl–Maslahah (AAM) Framework, connecting three normative principles with five governance functions: data stewardship, human-in-the-loop decision making, fairness and inclusion, transparency and verification, and capability and continuous evaluation. The framework positions AI as an analytical and administrative support system while retaining moral authority, high-stakes decisions, and institutional accountability with human leaders. Its novelty lies in shifting the discussion from technology adoption to an operational governance architecture that integrates efficiency, accountability, justice, and public benefit in Islamic educational settings. The framework offers a practical basis for institutional policies, standard operating procedures, leadership development, and future empirical research across madrasahs, pesantren, and Islamic schools.