Joseph Michael Schreiber, 32, will be charged with arson, and a hate-crime enhancement will be added to the charge, meaning it will be classified as a first-degree felony.
As a person who was imprisoned for a felony previously, Schreiber could face a sentence of 30 years, if convicted. But he also could face up to life in prison as a habitual offender, authorities said Wednesday.
Schreiber was still being questioned by investigators, Thompson said.
"An examination of his social media account shows multiple anti-Islamic points and comments," Thompson said.
The major said tips from callers and surveillance video led to the arrest.
The fire broke out late Sunday at the Islamic Center of Fort Pierce. Mateen, who killed 49 people at the Orlando nightclub in June, had attended the mosque.
No one was inside when the fire started, authorities said. St. Lucie County responded to the blaze around 12:31 a.m., after two drivers called 911 to report flames on the building's roof.
A man riding a Harley-Davidson-style motorcycle, possibly with saddlebags, was seen driving away.
Mateen had attended the Fort Pierce Islamic Center since 2003, Imam Syed Shafeeq Rahman told CNN earlier this year. Mateen had usually come for Friday prayers before the rampage at the Orlando nightclub on June 12.
Rahman said the mosque preached a peaceful message.
"So far as we here in Fort Pierce are concerned, we are always very conscious -- consciously speaking about peace, about love, about unity," Rahman told CNN in a previous interview. "We came to this country; this country gave us everything."
The mosque had also been attended by Moner Mohammad Abu-Salha, a Florida man who became the first known American suicide bomber in Syria.
One of the mosque's attendees told CNN that the Fort Pierce Islamic Center was "like any other mosque."
"It's simple, friendly," Bedar Bakht said in June. "Our imam is very good at explaining things. We never hear any stupid things coming out from anybody. It's very low-key."