It is not necessarily a disease, but more like a side effect of over consumption of Beta-Carotene. It is called "carotenodermia".
Read this wiki article about it:
"The most common side effect of excessive β-carotene consumption is carotenodermia, a harmless condition that presents as a conspicuous orange skin tint arising from deposition of the carotenoid in the outermost layer of the epidermis. High doses of β-carotene have been associated with increased rate of lung cancer among those who smoke."
|Includes CC-BY-SA content from Wikipedia's Beta-Carotene article (authors)|