This paper examines how the digital civility (morality) of contemporary Indonesian Muslim interaction on social media. The gap in Muslim behaviour on social media with the teachings of the Qur'an is caused by negative prejudice or sadistic behaviour; therefore, the values of Qur'anic digital civility are degraded. The research method used is a literature review examining Muslim interaction on social media such as Facebook, Twitter and YouTube. Contextual hermeneutics is used to analyze the interaction patterns of Muslims on social media. This research shows that Muslim interaction patterns on social media fall into the disassociation category, leading to incivility. One of incivility is flaming (verbal attacks in the form of blasphemy and insults); this is proven by hateful posts on social media. This behaviour pattern in social media is far from Qur'anic values which call for good speech, honesty and avoiding hoaxes; the words used must be courteous, put forward the principles of appropriateness and decency, and smooth and soft. These values of Qur'anic teaching are called digital Qur'anic civility