No injuries were reported but three workers were believed to have been rescued from the building.
Beirut-headquartered Arabian Construction Company won the contract to build the complex in 2014, according to its website.
Thick smoke from the fire filled the sky of Dubai.
Flames were still seen later Sunday morning coming from the podium level of the structure.
A witness of the fire, Anthea Ayache, told local media that firefighters responded quickly.
A 60-storey skyscraper under construction near the world's tallest tower Burj Khalifa was engulfed in a blaze Sunday, leaving four people injured and causing traffic jams Dubai.
Large numbers of firefighters were on the scene, and police cordoned off nearby roads.
Dubai Media Office confirmed the incident, stating the blaze broke out in the Fountain Views towers, with Dubai Civil Defence authorities launching cooling operations around 8.45am. Experts believe that much of those fires were caused by a popular cladding covering that is highly flammable.
"There's so many fire brigades, so they seem to have gotten on top of it very quickly", she said.