Does Madrid have a large market like La Bouqueria in Barcelona? If so, where is it located?

I don't know that Barcelona market, but, if you are speaking on food, flowers and the like, you can go to "mercado Maravillas", a big, competitive market that has a small entrance in the Bravo Murillo street, metro Alvarado or Estrecho.

Everybody knows the place, if you ask in the area (but for newcomers).

There's another small outdoor market in Barajas pueblo: coming into Barajas on Avda. de Logroño past the roundabout it's on your right.
Sorry, I don't know what days it is open.

Madrid doesn't have a market quite like the Boqueria--instead it has many more covered markets spread all over the city (every neighborhood has at least one or two) or little streets/alleys that are lined with food stores.

The market in my neighborhood (Mercado de la Cebada) is really great on Saturday mornings, though pricier than some of the other markets. During the week it is more scaled back, though still big by US standards.

Mercado San Miguel (right next to Plaza Mayor) is quite small, but has some interesting stalls--particularly the wild mushroom guy.

Other good markets that I've been to or heard about: Chamartin, Tetuan, Mostenses, Maravillas, La Paz...