Artificial intelligence tools that detect, infer or simulate emotion are rapidly entering the leadership toolkit, promising earlier detection of burnout, personalised check-ins and scalable care. Yet when empathy is increasingly mediated by algorithms, core relational qualities of leadership—authenticity, trust and psychological safety—can be put at risk. This paper explores the dark side of AI-enabled empathy by conceptualising an algorithmic empathy–authenticity gap: a disconnect between the growing volume and precision of empathetic signals and employees’ sense that those signals are genuinely felt and humanly owned. We identify four mechanisms that widen this gap—predictive emotional surveillance, synthetic emotionality, empathy inflation and relational displacement—and show how each reshapes emotional labour and leader–employee relationships. Building on these mechanisms, the paper outlines governance and design strategies that position AI as assistive rather than substitutive, safeguard emotional privacy and deliberately reconnect employees to human support. The argument reframes empathetic leadership as a socio-technical practice in AI-rich workplaces.