The goal is to create a systemic risk profile of companies during the COVID-19 crisis, which reflects their cause-and-effect relationships and risk management. The research objects are the following types of risks for companies listed in “Global-500” (Fortune) and the top 55 most competitive digital economies of the world (IMD) in 2017–2022: (1) risk of reduction in competitiveness (rank), (2) risk of reduction in revenue, and (3) risk of reduction in profit. The research methodology is based on the method of structural equation modelling (SEM), which allowed for exploring the cause-and-effect relationships between risk changes and digital risk management for companies during the COVID-19 crisis. As a result, based on the SEM model, it was proven that risks for companies during the COVID-19 crisis only slightly increased compared with that at the pre-crisis level. It was determined that companies faced large risks during the COVID-19 crisis in developed countries. It was discovered that, due to successful adaptation, risk management of companies assuaged the manifestations of the COVID-19 crisis in the economy. The key conclusion is that, under the conditions of a crisis of a non-economic nature (e.g., the COVID-19 crisis), companies independently and successfully manage their risks with the help of measures of digitalisation: corporate risk management with the limitation of state intervention is preferable. The contribution to the literature consists of the development of the concept of risks for companies by clarifying the specifics of risks and risk management of companies during the COVID-19 crisis. The theoretical significance lies in the fact that the authors’ conclusions rethought the risks for companies under the conditions of a crisis given the special context of a crisis of a non-economic nature (via the example of the COVID-19 crisis). The practical significance is that the developed novel approach to risk management of companies through digitalisation, which is based on the experience of the COVID-19 crisis, will be useful for risk management of companies under the conditions of future crises of non-economic nature caused by epidemics/pandemics and/or environmental disasters.