We investigate how universities’ research quality shapes their engagement with industry. Previous research has predominantly found a positive relationship between academics’ research quality and their commercialization activities. Here we use industry involvement measures that are broader than commercialization and indicate actual collaboration, i.e. collaborative research, contract research and consulting. We hypothesise that the relationship between faculty quality and industry engagement differs across disciplines, depending on complementarities between industrial and academic work, and resource requirements. Using a dataset covering all UK universities, we find that in technology-oriented disciplines, departmental faculty quality is positively related to industry involvement. In the medical and biological sciences we find a positive effect of departmental faculty quality but establish that this does not apply to star scientists. In the social sciences, we find some support for a negative relationship between faculty quality and particularly the more applied forms of industry involvement. The implication for science policy makers and university managers is that differentiated approaches to promoting university–industry relationships are required.