The increasing integration of Artificial Intelligence (AI) into corporate governance structures has transformed the manner in which companies undertake decision-making, risk assessment, compliance management, and strategic planning. While algorithmic systems enhance efficiency and predictive capabilities, they simultaneously create complex legal and governance concerns relating to transparency, accountability, fiduciary obligations, and regulatory oversight. This paper critically examines the legal implications of algorithmic corporate governance in India, with particular emphasis on the accountability of corporate boards and directors under the Companies Act, 2013. The study specifically analyses whether the fiduciary duties prescribed under Section 166 of the Act extend to AI-assisted decision-making processes and whether directors may be held responsible for harms arising from opaque or biased algorithmic systems. The research adopts a doctrinal and comparative methodology based upon statutory interpretation, judicial precedents, regulatory materials, and academic scholarship. In addition, the paper undertakes a comparative analysis of the European Union AI Act framework to evaluate evolving international standards concerning AI governance and corporate accountability. The study further examines issues relating to data governance, consumer protection, algorithmic bias, and regulatory compliance in AI-driven corporate operations. The paper argues that the existing Indian corporate governance framework remains insufficient to address the unique risks posed by algorithmic governance systems. It proposes the introduction of AI-specific corporate governance obligations, enhanced disclosure standards, board-level oversight mechanisms, algorithmic audit requirements, and clearer statutory liability principles to ensure responsible and accountable deployment of AI technologies within corporate entities.