There is a disease that makes it impossible to feel pain.

Congenital insensitivity to pain with anhidrosis, or CIPA, is a very aptly named disorder. It is congenital, which means it’s non contagious. Androhisis is a disorder that prevents sweating.

Often misdiagnosed as leprosy, CIPA is so rare that there are only eighty-four documented cases in the US, and only two in New Zealand. Though Japan has a higher 300, this is still very small. 

A disorder of the nervous system, CIPA entirely prevents the sensations of pain, heat, cold, or even the need to urinate. Those who have CIPA often injure themselves in ways that would normally be prevented by feeling pain. 

The most common physical injuries are injuries on the arms, legs, and mouth. Infection and scarring of the tongue is also common, as well as of the lips and gums. Ongoing infections of bones and joints are also common. 

Joint deformities can also occur, which often lead to amputation. Patients typically also have eye related issues due to rubbing them too hard. Because of the inability to sweat, hyperthermia is can happen during hot weather, which can lead to mental retardation. 

(Source)