While previous entrepreneurship research has only seldom drawn on organizational ambidexterity, the analysis of the important contemporary tensions among entrepreneurship, innovation management and strategic management issues may be facilitated by more closely analysing organizational ambidexterity in entrepreneurial settings. In this paper, we follow this thinking and more closely analyse an often applied form of corporate entrepreneurship: automation. Such automation is transferring work that was formerly conducted by humans to machines and may thus result in new tensions between corporate entrepreneurship, innovation management and the management of organizational stakeholders such as employees. The present paper investigates whether increased automation lowers the stability of firms’ relationships with their employees. In addition, we expect that this relationship is moderated by organizational ambidexterity, as employees may have perceived ambidexterity as a signal that their firm will not overly invest in exploitation only, but maintain a balance between exploitation and exploration. Drawing on stakeholder theory, previous insights into corporate entrepreneurship and a survey of German Mittelstand firms, our findings show that highly ambidextrous firms are indeed more vulnerable to automation, leading to lower employee relational stability. Our findings thus suggest that in highly ambidextrous firms, novel tensions around automation-related corporate entrepreneurship will be detrimental to the stability of the firm’s relations with one of its key stakeholder groups: employees.