The COVID-19 pandemic has disordered the educational process across the globe, as schools suddenly had to provide their teaching in an online environment. One question that raised immediate concern is the potential impact of this forced and rapid digitalization on inequalities in the learning process by social class, migration background and gender. Elaborating on the literature on the digital divide, we study inequalities in multi-level digital readiness of students and schools before the pandemic took place. Using data from the International Computer and Information Literacy Study (ICILS) on seven countries, and the Teaching and Learning International Survey (TALIS) on 45 countries, both from 2018, we demonstrate that schools and students vary in their readiness for digital education. However, school variation in digital readiness is not systematically related to student composition by SES and migration background. We thus find little evidence for a hypothesized ‘multi-level’ digital divide, which would result from systematic gradients in the readiness of school environments for digital education by student composition. More important drivers for a digital divide during the COVID-19 pandemic are the ICT skills students have, which are strongly related to students’ socioeconomic background. For digital education to be effective for every student, it is important that schools focus on improving students’ digital skills.