In a Facebook posting late Monday, the family announced that Zachary Reyna's organs were going to others who were "waiting on a miracle."
"Zac is our miracle," the family's Facebook posting said. "His spirit will always be among us. He changed all of our lives, brought us closer to God, strengthened our family and his story has touched people around the world."
Reyna became infected Aug. 3 while knee boarding with friends in a ditch near his family's LaBelle home. Doctors in Miami told the family late last week that the boy had extensive brain damage.
The family also noted on the Facebook page created to provide updates on the child's condition that funeral arrangements had not yet been made.
Miami Children's Hospital spokeswoman Jennifer Caminas wouldn't confirm whether the child has died, but she said Miami Children's Hospital "expresses heartfelt condolences to this devoted family. We respect the family's wishes and honor their privacy at this time."
The boy's uncle, Homer Villarreal, told The Associated Press on Saturday that the family was still reeling from the loss of a boy with boundless energy. He said the boy had challenged him to a basketball game two days before he was admitted to the hospital.
"It's hard for me to believe that Zachary can be laying in bed when this kid would never run out of energy," Villarreal said. "It's hard for all of us to believe this is happening to him."
The brain infection is called primary amebic meningoencephalitis. It destroys brain tissue and is usually fatal.
Infections from the amoeba are rare. Florida officials cited federal statistics showing that 28 infections were reported in the U.S. from 2003 to 2012, mostly from exposure to contaminated recreational water. A person cannot be infected with the amoeba by drinking contaminated water, state officials said, and the amoeba is not found in salt water.
Victims typically are exposed while swimming or doing water sports in warm ponds, lakes, rivers and canals during the hot summer months, mostly in the South.