A person with a burning sensation of the extremities usually has irritation or inflammation of the skin, muscles, bones or joints in the arm. Simple extremity injuries such as muscle strains and ligament sprains may cause a burning sensation in the extremities. An infection of the skin called cellulitis can also cause a burning sensation of the extremities. Other important causes include peripheral vascular disease, peripheral neuropathy, diabetic nerve disease, multiple sclerosis, Raynaud's syndrome, drug side effect, disk disease in the neck, and herniated disk in the back.