This isn't the new one is it? It's the one to the South of the city.
Not really recommended for you to go, especially if you look particularly foreign. I heard the experience of a boyfriend of one of the girls on this board about his experience going -- he's Bolivian and theoretically could fit in well enough but said he felt uncomfortable despite going in his rough looking clothes etc -- that the sheer quantity of people is just dizzying, and hoardes of people pressing up against each other. Difficult to get in supposedly, you get dropped off by a bus ages away (assuming you have no car, and if you do, you're not going to take it there) and then have to walk the rest of the way in. Yes you can get bargains, but if you don't like crowds, if you already stand out here like a sore thumb, it's probably not a great idea to go. It is a great place to get pickpocketed though, with so many people pressing up against you, you won't notice at all.
If you go, go in a group. If you've got a foreign accent (other than another South american accent) good luck trying to go unnoticed. If you're a foreign girl, well, it's up to you, I wouldn't go myself. However a lot of those reasons have to do with the fact that if I can knowingly avoid it, I prefer not to contribute to sweatshops.
Let's put it this way -- millions of dollars go through that market each week -- no taxes paid on it -- the merchandise is all made in sweatshops either in South America or Asia. The clothes you could buy were probably made by someone who was conned into moving to Buenos Aires because their life would be better, and instead ended up trapped in a sweatshop somewhere around town with no passport, no money, no way out. It's bad enough that namebrand labels in Argentina have their things made in sweatshops (a few have been caught and fined, but doubt they have stopped) -- but a market like this you can pretty much guarantee your money is going straight to supporting them.