Steve "Doc" Hopkins, the owner of the zoo, said Rex has been at the facility for 35 years and is "typically very docile" and unlikely to pose a danger to the public.
"He doesn't go hunt for his food. He's never had to do that, I don't even think he knows how," Hopkins told WLUK-TV.
The zoo said in a Facebook post that Rex "has severe arthritis in his jaws making it very difficult to open his mouth more than an inch."
Rex is one of four alligators that live at the zoo. Hopkins said the animals at the zoo are typically exotic pets that were surrendered by owners who could no longer care for them.