ABC Hobart reported abalone diver Ben Allen spoke to witnesses who said the family were cleaning fish on the boat when the attack occurred.
"All of sudden, the shark's leapt clean out of the water and it's grabbed the little boy and pulled him straight in," Allen told the ABC.
"But as he's pulled him in, it's obvious the shark's let go.
"The father, with his natural instinct I suppose, has leapt in straight after his son and managed to grab him."
"Congratulations to dad. Top fella, it's just a very very scary thing."
A North-West Coast woman, who aided the boy when he arrived at shore, said she was amazed by the child's bravery.
"My mother and I were walking along the beach and noticed a father carrying his son up the boat ramp looking very wet and I thought 'this doesn't look good'," the woman who wished to remain anonymous said.
"We raced into a nearby store where we found a first aid kit and addressed his injuries while the father spoke on the phone to paramedics as we waited for them to arrive.
"The father was clearly shaken and the little boy was in shock but was in incredibly good shape. He was able to talk to us and answer questions, which was remarkable.
"Speaking with the other two people on board I was told the shark was very big and it caused significant damage to the boat after it hit it hard and grabbed the child."
Police earlier on Friday warned of a large shark off the coast near Stanley. There is speculation it may have been a great white shark but that has not been confirmed.
Stanley fisherman Steve Hursey described the shark attack as a "freak accident".
"It's just unheard of," he said.
"I'm 28 years old and have been fishing all my life and never have I even seen a shark here, let alone a shark attack. We don't normally get them up here.
"I have heard of shark attacks occurring before but have never heard of anyone being pulled out of a boat."
Hursey said he was told the shark caused damage to the boat, which led him to believe the shark must have been more than 3m in size.
Circular Head mayor Daryl Quilliam said the child's shark attack had been the "talk of the town" on Friday afternoon.
"It's such a rare event. I'm not aware of any other shark attacks that have ever occurred in our district," he said.
"Thankfully the father jumped in to save his child, and the boy is now in a stable condition."
Quillam said he expected the Stanley community to rally behind the boy and his family.
- Adelaide Advertiser