Women (compared to men) and individuals from minority ethnic groups (compared to the majority group) face unfavourable labour market outcomes in many economies(1,2), but the extent to which discrimination is responsible for these effects, and the channels through which they occur, remain unclear(3,4). Although correspondence tests(5)-in which researchers send fictitious CVs that are identical except for the randomized minority trait to be tested (for example, names that are deemed to sound 'Black' versus those deemed to sound 'white')-are an increasingly popular method to quantify discrimination in hiring practices(6,7), they can usually consider only a few applicant characteristics in select occupations at a particular point in time. To overcome these limitations, here we develop an approach to investigate hiring discrimination that combines tracking of the search behaviour of recruiters on employment websites and supervised machine learning to control for all relevant jobseeker characteristics that are visible to recruiters. We apply this methodology to the online recruitment platform of the Swiss public employment service and find that rates of contact by recruiters are 4-19% lower for individuals from immigrant and minority ethnic groups, depending on their country of origin, than for citizens from the majority group. Women experience a penalty of 7% in professions that are dominated by men, and the opposite pattern emerges for men in professions that are dominated by women. We find no evidence that recruiters spend less time evaluating the profiles of individuals from minority ethnic groups. Our methodology provides a widely applicable, non-intrusive and cost-efficient tool that researchers and policy-makers can use to continuously monitor hiring discrimination, to identify some of the drivers of discrimination and to inform approaches to counter it.