The two-alarm fire was reported at 1:43 p.m. at Story Road and Roberts Avenue, near Happy Hollow Park and Zoo.
The zoo is located at 1300 Senter Road.
As of 3:20 p.m., a dispatcher said crews were still working to control the fire.
He said no structures are in danger and there had not been any injuries or other damage reported.
Around 2:20 p.m., Cal Fire crews were called to assist San Jose firefighters in battling the blaze, Cal Fire division chief Jim Crawford said.