Much of the conversations and practices of data governance emanate from technocratic and/or managerial lenses. This suggests a double bias towards (a) a linear teleological model of progress, (b) propelled by claims of objectivity and pristine scientific rationality inherent to Data. This paper seeks to move away from such approaches, to draw on the offerings of Critical Theory, to develop Critical Data Governance (CDG) as an approach that eschews objectivist, instrumentalist, and universalising tendencies. This, it does, by bringing to conversation the bodies of work on Critical Policy Studies and Critical Data Studies, in order to bring to the fore a multiplicity of policy actors, norms and values, interests and interactions, venues and deliberative sites, to the study of data governance and policymaking. Towards this, the paper showcases some examples from the South(s), and then moves on to present a provocation for CDG as a Southern Standpoint for Data, overcoming the inadequacies of Critical Theory and catering to anti-/de-colonial and anti-caste aspirations of peoples.