Armadillos are well known for being carriers of the leprosy disease. While this terrifies many people, they often only know of horror stories from ancient days and not what the disease really is. Leprosy is an infectious disease that leaves sores on the skin and can potentially result in nerve damage. While it was deadly in the past, it is a curable disease today. With all that said, yes armadillos do carry leprosy. However, you will not get it from just touching an armadillo. In fact, the most common way the disease is transferred is through consumption - as in EATING the armadillo. While this may seem strange, it is actually a common practice in rural areas.
Armadillos are not very likely to be carrying any other diseases, which is likely due to their low body temp. While it is extremely unlikely, you may come across an armadillo with rabies. An armadillo infected with rabies will not charge you or anything, but can be described as less shy than normal. They are also common carriers of tapeworms, which are shed in the feces of an armadillo and can be transferred to humans, causing extreme intestinal issues.
While armadillos carry significantly less diseases than other animals, they can be serious if contracted. This makes it necessary to take proper precautions when dealing with armadillos and their waste.