Abstract Many leaders communicate with their followers via electronic devices during non‐work time. However, prior research on information and communication technologies (ICT) in the workplace has largely neglected leaders' ICT use and its broader organizational implications. Guided by climate models of organizational functioning and effectiveness, we propose that the extent to which leaders use their smartphones after hours shapes organizational norms regarding employees' availability for and responsiveness to work‐related communication via electronic devices during non‐work time. Drawing from conservation of resources theory and the work–family literature, we develop and test an organizational‐level model in which leaders' after‐hours work‐related smartphone use is positively associated with an organizational climate of constant connectivity, which in turn impairs employees' collective well‐being. Findings from a large‐scale, multi‐source study of 5414 managerial and 17,962 non‐managerial employees in 142 German organizations support our hypotheses. Moreover, we show that the indirect health‐impairing effect of leaders' after‐hours smartphone use is weaker in more formalized organizations. Our study integrates and contributes to ICT and work‐family research by shedding light on the critical role of leaders in the emergence of shared availability norms in organizations and their implications for employees' collective well‐being.