More than 1,000 people were forced to flee the blaze, which is burning more than 15,200 hectares (38,000 acres) about 200 kilometres (124 miles) north of Los Angeles.
While the fire was nearing the park's protected groves of giant sequoia trees, it was not believed to be a threat to the 83.8-metre (275-foot) General Sherman Tree, which is believed to be the world's largest tree by volume.
Several hundred campers and Boy Scouts were forced to leave the park as the flames advanced.
"It has got good potential behind it to grow into a massive wildfire," Sequoia National Forest spokeswoman Denise Alonzo said.
Authorities believe the fire started Sunday afternoon, but its cause remains under investigation.
The area where the fire is burning has not had any rain since spring.
National guard
Wildfires have ripped through several parts of the United States and Canada in recent months, and several were still burning out of control.
In southern Oregon, National Guard troops were sent in to help stop a fire that had grown to more than 37,000 hectares (91,400 acres) and was threatening 65 homes.
Meanwhile, firefighters in Colorado are battling a blaze near Rocky Mountain National Park that has grown to more than 1,600 hectares (3,950 acres).
Hundreds of homes had to be evacuated, although higher humidity and a bit of rain have made fighting the fire easier.