Fire crews responded to a 911 call reporting that flames were coming out of the Fort Pierce Islamic Center, Major David Thompson of the St. Lucie County Sheriff's Office said.
Security video showed an individual approaching the building from the east, he said.
"Immediately after the individual approached, a flash occurred and the individual fled the area," Thompson said.
"Evidence has revealed that this fire was set intentionally," he said. "The sheriff's office is currently investigating this as an arson."
No injuries were reported and the extent of the damage was not immediately clear.
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Authorities were working on enhancing the security video to help identify the perpetrator.
Thompson declined to speculate on a motive, but noted that it came shortly after the 15th anniversary of the 9/11 terror attacks on the United States.
"We all know the implications of the date... Is that related? I would not want to speculate but certainly that is in the back our minds," he told reporters.
The attack also came as Muslims worldwide prepared to celebrate Eid al-Adha, Islam's feast of sacrifice.
Forty-nine people were killed and another 53 injured on June 12 when Mateen, a 29-year-old US citizen of Afghan origin, opened fire on the Pulse gay nightclub in Orlando. Mateen was killed by police.
The mass shooting was the deadliest in modern US history.
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