Nigeria's artificial intelligence (AI)-driven financial sector has expanded at extraordinary speed, with 87.5% of Nigerian fintechs deploying AI for fraud detection and 37.5% for credit scoring as of 2026, yet the regulatory framework governing these deployments remains materially inadequate relative to international best practice. This study provides the first systematically scored, five-domain AI governance gap assessment for the Nigerian financial sector, benchmarked against the EU AI Act, the NIST AI Risk Management Framework, the Financial Stability Board, and the International Organisation of Securities Commissions using a composite Nigerian AI Governance Coverage Score (NAIGCS) constructed from the Central Bank of Nigeria's Fintech Policy Insight Report, the NDPC General Application and Implementation Directive 2025, the FCCPC Digital Lending Regulations 2025, and the CBN's AML AI Guidelines 2026. Employing a qualitative documentary analysis methodology combined with a structured thematic coding framework across five governance domains model explainability, algorithmic bias testing, systemic risk governance, consumer protection, and institutional governance. The study finds a composite NAIGCS of 24% against a maximum possible score of 100%, with critical gaps in pre-deployment fairness testing, demographic outcome monitoring, and consumer AI decision explainability. Comparative analysis against eleven African and global jurisdictions reveals that Nigeria's regulatory trajectory is more advanced than Ghana and Zambia but substantially behind Kenya's Digital Credit Providers Regulations and South Africa's Intergovernmental Fintech Working Group framework. The study proposes a phased, context-specific Nigerian AI governance framework calibrated to the CBN's SupTech development trajectory and concludes that the current regulatory gap, if unaddressed, risks entrenching the very financial exclusion patterns that AI-driven financial services are promoted to solve.