According to Local Order No. 11 which was passed in 2003, littering cigarette waste in public or disposing it in undesignated bins could land a fine of 500 AED. Although passed in 2003, this order is being reinforced. According to Gulf News, there are currently 154 inspectors employed at the Waste Management Department at Dubai Municipality who are authorised to fine people for improper disposal of cigarettes.
Source: Dubai Municipality Facebook page