Abstract This paper analyses the impact of robots on workers' wages in the manufacturing sector, with a particular focus on relative wages for workers with different levels of education and in different occupations. Using high‐quality matched employer–employee register data with firm‐level information on the introduction of industrial robots, we identify the effects of robotization on relative wages within firms. Skilled blue‐collar workers with a vocational degree experience a decline in wages when firms introduce robots, while there are only small effects for the other groups of workers. These results suggest that robots are substitutes for tasks undertaken by skilled blue‐collar workers in manufacturing, and furthermore that the adoption of robots contributes to a polarization of the labour market and a hollowing out of the wage distribution, rather than to skill‐biased technical change.