Zoo staff ran to the scene but the gazelle, Raul, was already dead.
Zoo staffers described the animal's behavior as puzzling. The city says in a news release the zoo will run a necropsy and pathology evaluation to learn what might have caused the incident.
The Addra gazelle is a critically endangered species, with only 500 left in the wild.
It's the second rare gazelle to die at the zoo, where a 3-year-old Addra died of a sudden illness in December 2012.