Advances in robotics and artificial intelligence are increasingly enabling organizations to replace humans with intelligent machines and algorithms1. Forecasts predict that, in the coming years, these new technologies will affect millions of workers in a wide range of occupations, replacing human workers in numerous tasks, but potentially also in whole occupations. Despite the intense debate about these developments in economics, sociology and other social sciences, research has not examined how people react to the technological replacement of human labour. Our research begins to address this gap by examining the psychology of technological replacement. Our investigation reveals that people tend to prefer workers to be replaced by other human workers (versus robots); however, paradoxically, this preference reverses when people consider the prospect of their own job loss. We further demonstrate that this preference reversal occurs because being replaced by machines, robots or software (versus other humans) is associated with reduced self-threat. In contrast, being replaced by robots is associated with a greater perceived threat to one’s economic future. These findings suggest that technological replacement of human labour has unique psychological consequences that should be taken into account by policy measures (for example, appropriately tailoring support programmes for the unemployed).