Parsons said Stabile had been in the park's wave pool.
Fabrizio Stabile, 29, died September 21, according to his obituary.
"Our hearts and prayers are with his family, friends and the New Jersey surf community during this hard time", owner Stuart E. Parsons Jr. told the Waco Tribune.
If water containing the amoeba goes up the nose, the amoeba can invade and cause a rare and devastating infection of the brain.
The Centers for Disease Control and Prevention has since closed down the park and is testing the waters for the amoeba known as Naegleria fowleri (nee-GLEHR'-yah FOW'-lur-eye), the organism that was ruled as the cause of Stabile's death.
An obituary for Stabile describes him as an "avid outdoorsman" who "loved snowboarding, surfing, and anything to do with friends and family".
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The park is voluntarily closed until the test results come back.
He added: '"Our hearts and prayers are with his family, friends, and the New Jersey surf community during this hard time".
He said the surf resort, which operates an artificial man-made wave, is in compliance with the CDC's "guidelines and recommendations concerning Naegleria fowleri". It takes an average of five days for symptoms to appear exposure, with headache, fever and nausea the main symptoms.
The CDC says Naegleria fowleri is often found in warm freshwater.
Stabile's family has created the Fabrizio Stabile Foundation for Naegleria Fowleri Awareness "to bring awareness to, and educate as many people as possible about, this rare and preventable infection", they said on GoFundMe.
Only four people out of 143 have survived infection in the US from 1962 to 2017, the CDC said. Swallowing water contaminated by the amoeba can not cause the infection.