Data plays a critical role in the training, testing and use of artificial intelligence (AI), including in the military domain. Research and development for AI-enabled military solutions is proceeding at a rapid pace; however, pathways and governance solutions to address concerns (such as issues with the availability and quality of training data sets) are lacking. This paper provides a comprehensive overview of data issues surrounding the development, deployment and use of AI; examines data governance lessons and practices from civilian applications; and identifies pathways through which data governance could be enacted. The paper concludes with an overview of possible policy and governance approaches to data practices surrounding military AI to foster the responsible development, testing, deployment and use of AI in the military domain.