Officials said the person set off a smoke bomb at a nearby paintball park, triggering the fire.
The suspect claimed to have permission from the paintball park owners to set off the smoke bomb, but the owners denied to officials giving their permission.
The Towsley Fire was first reported around 1:40 p.m. near The Old Road and Towsley Canyon Road.
Officials said there are 15 structures along The Old Road threatened by the flames.
The Los Angeles County Sheriff's Department did not release the identification of the person in custody.
Los Angeles County firefighters battled the three-alarm blaze from the ground and the air.
The fire created plumes of thick, white smoke, which could be seen for miles.
There was little wind, so the fire was mostly driven by the hot and dry conditions as it burned up the hillside.
The Old Road was closed to traffic from Gavin Canyon to Calgrove Boulevard.
The nearby 5 Freeway was open to traffic, but cars on the southbound side were moving slowly past the thick smoke.
There were no immediate reports of any injuries.