In the ongoing coronavirus disease 2019 (COVID-19) pandemic, media reports have caused anxiety and distress in many. In some individuals, feeling distressed by information may lead to avoidance of information, which has been shown to undermine compliance with preventive health behaviors in many health domains (e.g., cancer screenings). We set out to examine whether feeling distressed by information predicts higher avoidance of information about COVID-19 (avoidance hypothesis) and whether this, in turn, predicts worse compliance with measures intended to prevent the spread of COVID-19 (compliance hypothesis). Thus, we conducted an online survey with a convenience sample (N = 1059, 79.4% female) and assessed distress by information, information avoidance, and compliance with preventive measures. Furthermore, we inquired about participants’ information seeking behavior and media usage, their trust in information sources, and level of eHealth literacy, as well as generalized anxiety. We conducted multiple linear regression analyses to predict distress by information, information avoidance, and compliance with preventive measures. Overall, distress by information was associated with better compliance. However, distress was also linked with an increased tendency to avoid information (avoidance hypothesis), and this reduced compliance with preventive measures (compliance hypothesis). Thus, distress may generally induce adaptive behavior in support of crisis management, unless individuals respond to it by avoiding information. These findings provide insights into the consequences of distress by information and avoidance of information during a global health crisis. These results underscore that avoiding information is a maladaptive response to distress by information, which may ultimately interfere with effective crisis management. Consequently, we emphasize the need to develop measures to counteract information avoidance.