Islamophobic hate speech on social media is a growing concern in contemporary Western politics and society. It can inflict considerable harm on any victims who are targeted, create a sense of fear and exclusion amongst their communities, toxify public discourse and motivate other forms of extremist and hateful behavior. Accordingly, there is a pressing need for automated tools to detect and classify Islamophobic hate speech robustly and at scale, thereby enabling quantitative analyses of large textual datasets, such as those collected from social media. Previous research has mostly approached the automated detection of hate speech as a binary task. However, the varied nature of Islamophobia means that this is often inappropriate for both theoretically informed social science and effective monitoring of social media platforms. Drawing on in-depth conceptual work we build an automated software tool which distinguishes between non-Islamophobic, weak Islamophobic and strong Islamophobic content. Accuracy is 77.6% and balanced accuracy is 83%. Our tool enables future quantitative research into the drivers, spread, prevalence and effects of Islamophobic hate speech on social media.