The Bronx Zoo

To my knowledge the term originated in the 70s-80s and it mainly referred to the team not the stadium.

During that era, there was lots of conflicts with players and the owner, George Steinbrenner. Players fought with each other, Steinbrenner fired poor Billy Martin a bunch of times and these antics became known as the Bronx Zoo.

Its usage seems to have grown with time. Bronx Zoo appears to also refer to the crazy things that happen at Yankee stadium, like the wild/rowdy fans.

However Yankee Stadium had been known as "The House That Ruth Built" for the longest time and most Yankee fans will refer to as such.