The exposure likely occurred at a splash pad at the Country Club of Little Rock, the department said.
Samples from the club’s pool and splash pad were sent to the Centers for Disease Control and Prevention (CDC), who confirmed that a sample from the splash pad had viable Naegleria fowleri.
The country club closed its pool and splash pad, and has been assisting authorities with the investigation, the ADH said.
The pools remain closed, and there is no ongoing threat to the public, it added.
Several Arkansas news outlets reported that they had confirmed that the victim was a child.
According to the CDC, Naegleria fowleri is found in soil and warn fresh water from lakes, rivers, pools and hot springs.
People become infected when water goes up their nose while swimming, the CDC said.
Early symptoms include headaches, fever, nausea and vomiting, followed by hallucinations and seizures.
There is no known cure for Naegleria fowleri, which kills on average three people in the United States each year.
The ADH stressed that the amoeba cannot be transmitted from human to human.
“It is important to maintain pools and splash pads by making sure that disinfection levels are appropriate and free of soil contamination,” the health department said.
The last known infection in Arkansas was in 2013.
In July, Georgia teenager Megan Ebenroth died after becoming infected with the amoeba while swimming in a lake near her home in McDuffie County.