The boy, Devin Funck, and two girls were playing in the water some 32 kilometers (20 miles) northeast of New Orleans when the three-meter long alligator attacked, WDSU TV said.
The reptile swallowed the boy's arm and tried to pull him under, but Devin managed to free himself by poking the alligator in the eye, his relatives said. The two girls were unhurt in the attack and called 911.
The animal was later shot and cut open by wildlife officials, and the boy's limb was subsequently retrieved from the alligator's stomach.
The boy was airlifted by helicopter to hospital. He is currently undergoing surgery to reattach the severed arm.