Mateen was killed by law enforcement officials after killing 49 people and wounding 53 others in a gay nightclub in Orlando in June.
Law enforcement officers received reports of flames rising from the Islamic Center of Fort Pierce, located about 100 miles (160 km) southeast of Orlando, at about 12:30 a.m. EDT, St. Lucie County Sheriff's Major David Thompson told reporters at a news conference. No one was hurt.
The attack occurred on one of the holiest Muslim holidays.
Surveillance video showed a white or Hispanic man riding up on a Harley Davidson-style motorcycle, Thompson said. The suspect got off the bike and approached the mosque carrying a bottle of liquid and papers, moments before the blaze erupted, he said.
"Immediately after the individual approached, a flash occurred and the individual fled the area," Thompson said.
Investigators have not identified the man, who shook his hand while leaving the area of the flames, indicating that he might have burned himself, Thompson said.
At a news conference, a spokesman for the Council on American-Islamic Relations in Florida said the blaze was an act of hate. Ahmed Bedier, president of the civic group United Voices for America, also called for authorities to investigate it as a hate crime.
Thompson said deputies will explore whether the arson was a hate crime.
Investigators, still seeking a motive, were considering a connection with the 15th anniversary of the Sept. 11 attacks on Sunday, Thompson said.
Eid al-Adha, a major Muslim holiday, was being celebrated on Monday and also could have prompted the attack, Thompson said.
"For this to happen to us, on the morning of our biggest celebration of the year, was something horrific," Hamaad Rahman, associate imam at the mosque, said at a news conference.
"Our community is bigger than a building, we are stronger than that," he added. "Hopefully as time goes by, we will be able to rebuild."
The mosque temporarily relocated its morning prayers for Eid al-Adha, also known as the Feast of Sacrifice.
The mosque in Fort Pierce, identified as Mateen's place of worship, has reported threats of violence and intimidation. In June a motorcycle gang circled the center and shouted at its members, and in July a Muslim man was beaten outside the mosque.
Mateen told police in a 911 call that he had pledged allegiance to the head of the Islamic State militant group, though investigators do not believe he had help from outside organizations.