Perez was fishing in the surf when the shark surprised him, biting him once on his right arm and twice on the right leg.
He is in fair condition at the hospital, where he was airlifted after being wounded.
"He is doing very well," says microsurgeon Dr. Emmanuel Melissinos. "He has good circulation to his hand. He is in stable condition. We'll try to get him out of the ICU today and get him to a regular room."
The attack happened while the boy, his father, Blas Perez, and Don Townes of Lake Jackson were fishing for trout at Bryan Beach, near Freeport.
There was a group of trout and dolphins all around them and they were just catching the trout with artificial bait, Townes tells The Early Show co-anchor Rene Syler.
But the innocent evening of fishing turned into a terrifying nightmare. Townes recalls, "We were only about 50 yards from the beach and the water was only a little over my knees and it was up to Aaron's waist and the fish went down and I hollered at Aaron, who was about 20 yards from me and his dad was 20 yards on the other side of Aaron. And I said, 'Where did the fish go?' He said, 'They're all around me.' About that time, the shark hit him," Townes explains.
Dr. Melissinos says, "Apparently, the shark caught the entire hand and wrist." The forearm was locked in the shark's jaws.
Townes and the boy's father reached the boy and scared away the shark.
Townes recalls, "His dad started screaming, running at him, and I run from the other direction. And the screams sounded pretty good so I started emulating it and we run to it and started beating on the shark with the rods because it had Aaron by the arm at that time, and when he turned loose, his dad was beating on it on his side because he was on the shark's side. I grabbed the boy and saw the injury and clamped off his arm above his elbow with my hand and held it and took him to the beach."
The boy was taken to the Freeport fire station, which is about an hour and a half drive from Houston. Emergency officials arranged for him to be flown by helicopter to Memorial Hermann Children's Hospital.
When Dr. Melissinos first saw Aaron, he says, the damage was pretty extensive. He says, "When his dad, Don and the boy hit it quite hard, it let go, but it produced some more damage to the hand, but fortunately let him go. But it just created a lot of injury to the forearm. The hand was just holding by the crushed bones."
Freeport Fire Chief John Stanford described the shark as a bull shark, which is aggressive and swims in shallow water.