Armadillos can catch leprosy.

Strangely enough, in the 1960s scientists were researching leprosy by injecting the disease in armadillos for experiments. However, they found that many of the armadillos already had it.

Leprosy has been found in certain chimps and monkeys but this is very rare. Armadillos are the only animals besides humans that have significant numbers of leprosy cases.

Don't worry about catching leprosy from an armadillo, though. Only about 5% of them have leprosy, and leprosy is in decline around the world. Supposedly, 95% of humans are immune to leprosy anyway.
(source)