Previous research has argued that fake news may have grave consequences for health behaviour, but surprisingly, no empirical data have been provided to support this assumption. This issue takes on new urgency in the context of the coronavirus pandemic. In this large preregistered study (N = 3746) we investigated the effect of exposure to fabricated news stories about COVID-19 on related behavioural intentions. We observed small but measurable effects on some related behavioural intentions but not others – for example, participants who read a story about problems with a forthcoming contact-tracing app reported reduced willingness to download the app. We found no effects of providing a general warning about the dangers of online misinformation on response to the fake stories, regardless of the framing of the warning in positive or negative terms. We conclude with a call for more empirical research on the real-world consequences of fake news.