The Zoo just recently put a policy into place where they no longer allow visitors to bring food and beverages into the Zoo. Water bottles are ok, as is baby food/infant formula, and food for those with dietary needs. I haven't been there since they did it, but it sounds like they aren't actively enforcing it by searching bags at the entrance - all they have done is put up a sign.
Here's a link to the article about it:
http://www3.signonsandiego.com/stories/2009/feb/05/1n5zoo233859-zoo-picnic/?metro