During COVID-19, governments and the public are fighting not only a pandemic but also a co-evolving infodemic-the rapid and far-reaching spread of information of questionable quality. We analysed more than 100 million Twitter messages posted worldwide during the early stages of epidemic spread across countries (from 22 January to 10 March 2020) and classified the reliability of the news being circulated. We developed an Infodemic Risk Index to capture the magnitude of exposure to unreliable news across countries. We found that measurable waves of potentially unreliable information preceded the rise of COVID-19 infections, exposing entire countries to falsehoods that pose a serious threat to public health. As infections started to rise, reliable information quickly became more dominant, and Twitter content shifted towards more credible informational sources. Infodemic early-warning signals provide important cues for misinformation mitigation by means of adequate communication strategies.