Carl James Dial Jr., 23, was booked into Riverside County Jail. He has not been formally charged but police said he was arrested on suspicion of arson, a hate crime and felony burglary.
Dial's bail was set at $150,000, according to online jail records. He is scheduled to appear in court Wednesday morning. It was not immediately clear Saturday whether Dial had an attorney.
The fire at the Islamic Society of Coachella Valley began Friday just after noon. Police said the fire was "an intentional act."
Four or five people were praying inside the mosque when the fire started, Riverside County Supervisor John Benoit told CNN affiliate KMIR
Nobody was hurt and the fire was quickly extinguished, though it caused smoke damage throughout the building, authorities said.
The FBI is investigating along with local authorities, said Laura Eimiller from the agency's Los Angeles division.
Benoit said an incendiary device may have caused the fire.
"Terrorism should not beget terrorism and that's what this would be if in fact there was someone who threw a device in this mosque with the intention of destroying the mosque or hurting the people inside who were praying," Benoit said.
The mosque has had an armed security guard since a shooting last year.
On November 4, 2014, someone fired four shots toward the Coachella mosque during the early morning hours while four people prayed inside, KMIR reported. Three bullets struck a vehicle, two hit the building and one lodged in a fence on the property but nobody was injured. No arrests have been made, KMIR said.
A study by the group reported at least 63 acts of vandalism, harassment and anti-Muslim bigotry through December 8, three times more than last year and the highest number of incidents since the group began keeping track in 2009.
Authorities blocked people from entering the Coachella mosque while the investigation was underway. A group gathered on the sidewalk outside the crime scene tape and knelt in prayer.
Alisa Shabazz told KMIR the fire happened shortly before a big crowd of people arrived for weekly prayer. She wondered aloud why somebody would attack her house of worship.
"We're peaceful people," she said. "We don't terrorize people."
Coachella is about 30 miles from Palm Springs and about 80 miles from San Bernardino, where Tashfeen Malik and Syed Rizwan Farook fatally shot 14 people December 9
. Farook's father said his son supported ISIS.