The fire started at about 2:10 p.m. on Silver Creek Valley Road near Fontonoso Way, a fire dispatcher said.
The blaze was contained at 4:15 p.m., according to Stallard, who said crews would continue to fight the fire until it gets dark tonight.
Because of a lot of dry vegetation in the area surrounding the fire, "we're planning on being here for a while," Stallard said.
However, dangerous conditions, including the possibility of falling tree branches and rattlesnakes near Coyote Creek, will prevent firefighters from battling the blaze overnight, Stallard said.
A firefighter from Cal Fire was transported to a local hospital for heat exhaustion from the fire, according to Stallard.
Cal Fire is assisting at the scene with a helicopter and two tankers, while the Santa Clara County and Milpitas fire departments and the South County Fire Authority are also assisting San Jose firefighters, Stallard said.
The blaze is a TIER 2 fire, Stallard said. TIER stands for Tactically Integrated Emergency Response, and Stallard said a TIER 2 fire means that the San Jose Fire Department has at least 35 units at the scene.