Universities face increasing demands to improve their visibility, public outreach, and online presence. There is a broad consensus that scientific reputation significantly increases the attention universities receive. However, in most cases estimates of scientific reputation are based on composite or weighted indicators and absolute positions in university rankings. In this study, we adopt a more granular approach to assessment of universities' scientific performance using a multidimensional set of indicators from the Leiden Ranking and testing their individual effects on university Wikipedia page views. We distinguish between international and local attention and find a positive association between research performance and Wikipedia attention which holds for regions and linguistic areas. Additional analysis shows that productivity, scientific impact, and international collaboration have a curvilinear effect on universities' Wikipedia attention. This finding suggests that there may be other factors than scientific reputation driving the general public's interest in universities. Our study adds to a growing stream of work which views altmetrics as tools to deepen science–society interactions rather than direct measures of impact and recognition of scientific outputs.