The AI Act advances a risk-based approach to the legal regulation of AI systems in the European Union. While we support this development, we argue that adequate AI governance requires paying attention to the broader implications of AI systems on the socio-technical landscape in which they are designed, developed, and used. In addition to risk-based impact assessments, this involves coming to terms with the socially disruptive implications of AI, which should be governed and guided in a dynamic ecosystem of regulation, law, ethics, and evolving human practice. In this paper, we outline a ‘social disruptiveness-based’ approach to AI governance aimed at addressing disruptions by AI that are not easily captured by legal regulation, but that are nonetheless of great societal and ethical concern. We argue that integrating the AI Act risk-based approach with a social disruptiveness-based approach can offer a more nuanced understanding of the dimensions of impact of AI systems on society at large, thus enhancing the governance of AI and other socially disruptive technologies.