The recent field of Corporate Digital Responsibility (CDR) calls for multi-stakeholder collaboration and effort of all, including Higher Education Institutions (HEIs). To explore the role of HEIs and their potential contribution to digital responsibility competence, this study examines whether and how HEIs are addressing corporate digital responsibility in marketing and business postgraduate courses. The primary purpose is to raise awareness of digital responsibility and digital responsibility competence in the context of HEIs. Through an exploratory approach, it examines whether and how digital responsibility is addressed in marketing and business postgraduate courses. Inspired by constructive alignment and backwards design principles, it focuses exclusively on the course curricula’ descriptions and learning outcomes. Based on a sample of 22 courses, the results demonstrate that digital responsibility needs to be made much more explicit, visible, real and relevant. For advancing the discussion on how to address digital responsibility in business education, the authors call for further studies on how we, as educators, can contribute more actively and more effectively to bring digital responsibility to the surface and forefront of learning, pedagogy and curriculum design.