If the animal you're trying to shoot is close to the front fencing, there isn't really much you can do. If it's toward the back of the enclosure, using a long lens and a wide aperture will cause the wire to fall so out of focus as to be invisible. You should try to get as close to the wire as possible without breaking any of the zoo's rules...
The other thing to consider is where the light is coming from. If the sun is falling on the wire, it's going to be brighter and will act like a big diffuser, causing the image to have a lower contrast. It's best to shoot through wire that is shaded. You're also going to run into the same problem if you try to use flash to add some light to the picture. It's best to get the flash off and above the camera by using a cord.