I think maxtorres91's response was a little overblown. Being aware of the chance of injury is smart thing, especially when it comes to training. Besides, you need to know your present limits in order to overcome them. Not to mention that although sports like swimming lack contact, you can still screw up your body if you don't train and compete correctly.
In terms of your chance of injury in wrestle, it's certainly a contact sport. In wrestling particularly, there is a greater chance for head/neck/spine injuries, as well as limb injuries dislocations, sprains, strains, and some breaks then you'd see in other sports. Some of these limb injuries can be quite serious, at the knee and shoulder joints specifically. Another consideration is the very real possibility of developing an eating disorder in order to make weight. In gymnasts, boxers, and wrestlers specifically, this is something that athletes need to acknowledge in order to know and prevent such developments.
But like I said before, all athletic activities come with some level of risk. I ended up with 6 concussions, a broken hand, broken ribs, dislocated patella, fractured neck, and countless stupid small injuries across ice hockey, football, track and field, and baseball. In the end, if you truly enjoy the competition, you can work through injuries and return to those activities. It's almost a litmus test for how much you like the sports you've committed yourself to.