This study systematically reviews the convergence of Artificial Intelligence (AI), Bayesian learning, and Sharia principles within the domain of Islamic financial analytics and entrepreneurial innovation. Using the PRISMA protocol, 523 records were initially identified from Scopus and Web of Science databases, resulting in 68 studies that met the inclusion criteria. The review applies the PICOS framework to guide the research questions, focusing on AI applications, methodological integration, and the ethical alignment of Bayesian inference with Sharia law. The findings reveal that while AI has been increasingly applied to enhance financial inclusion, risk assessment, compliance automation, and operational efficiency in Islamic finance, Bayesian learning methods remain underutilized. Most existing research focuses on general AI models, such as machine learning and predictive analytics, but lacks probabilistic frameworks that reflect Sharia's ethical treatment of uncertainty (gharar) and speculation (maysir). Furthermore, the literature shows limited integration of maqasid al-Shariah (objectives of Islamic law) as performance indicators, insufficient comparative studies with conventional finance, and fragmented methodological coherence. This review highlights the need for the development of Bayesian-Sharia alignment frameworks and adaptive governance models that integrate ethical transparency with analytical rigor. Future research directions include AI ethics grounded in Islamic epistemology, AI-assisted issuance of fatwas, probabilistic compliance modeling, and the establishment of unified regulatory standards for intelligent Islamic finance systems. The study concludes that harmonizing technological innovation with spiritual accountability can position Islamic finance as a model for sustainable, transparent, and ethically driven global financial development.