The flagging of false news has been one of the ways suggested to discourage people from sharing deceiving news stories on social media, and recent years have seen a growing number of initiatives focused on providing credibility labels for news online. Using an experimental design, this study assesses the effectiveness of such labels designed to reduce the sharing of false news. Specifically, it examines the impact of warning labels on Facebook users’ intentions to share false news stories, drawing on a sample of 501 participants from across the political spectrum. The study also explores users’ perceptions of the likelihood that other people would share false news even after seeing a warning label. We find that the flagging of false news may indeed have an effect on reducing false news sharing intentions by diminishing the credibility of misleading information. Furthermore, we find that users may be prone to believing that others are more likely to share false news than themselves, confirming the third‐person effect. This study shows that flagging of false news on social media platforms like Facebook may indeed help the current efforts to combat sharing of deceiving information on social media.