The emergence of AI-enabled applications has drawn attention to the need for AI governance. This essay builds on organizational governance literature and proposes a framework for developing organizational governance structures. Following a call to incorporate all stakeholders in governance [1], the framework considers the interests of all organizational stakeholder groups. In addition, it delineates five types of AI-related organizational decisions, which have the potential to significantly impact stakeholder interests. Furthermore, the framework considers four distinct outcomes and byproducts of AI which may impact the distribution of stakeholder benefits and risks. These need to be specifically addressed by organizational AI governance structures. We contend that the details furnished by the framework pave the way for future research on AI governance, adaptation in an AI-driven organization, and AI-related legal framework development.