The rapid advancement of generative and autonomous AI has intensified debates over AI governance worldwide. Existing frameworksincluding the EU AI Act and Japan's AI Business Guidelinesprimarily evaluate AI along the axes of technical safety, fundamental rights protection, and algorithmic transparency. While these are necessary conditions for responsible AI, they are insufficient: they do not systematically address how AI reshapes the social structures within which individuals live. This paper identifies a critical gap in current AI governancethe absence of any evaluation framework for AI's impacts on social stabilityand proposes a new institutional mechanism to fill it: the AI Social Impact Assessment (AISIA). Modelled on Environmental Impact Assessment regimes, AISIA would mandate prior assessment and ongoing monitoring of large-scale AI systems along four social stability indicators: power concentration, social fragmentation, institutional trust erosion, and exclusion. The paper situates AISIA in relation to the EU AI Act and OECD AI principles, proposes two pilot implementation scenarios, and argues that social stability is not merely an ethical concern but a structural precondition for sustainable technological development. Note: The research design, arguments, and conclusions are the author's own. AI writing assistance was used in the drafting of this paper.