A tiger with down syndrome made the news a while back.
That's a dumbed-down explanation from a third-rate viral site, which exists solely to generate clicks from Facebook, and not an actual medical or scientific description of the tiger's condition.
Edit: It looks like the very definition of Down Syndrome (three copies of the 21st chromosome instead of two) doesn't really allow for an "animal version", since the 21st chromosome is specific to humans.