Islam is an Abrahamic religion following the writings in their religious text, the Qur'an. The followers of Islam (Muslims) believe the Qur'an is the word of God (Allāh). They believe that the last prophet is Muhammad.
The Qur'an is against idolatry, which Muslims interpret in a way which disallows depictions of Allāh and Muhammad. This rule stands for non-muslims as well as muslims. There have been some famous backlashes about depictions of Muhammad such as an incident against the creators of South Park, the murder of Theo van Gogh and the shooting at Charlie Hebdo.