Governor Brown declared an emergency for San Francisco because of the wildfire's threat to utilities.
The fire nearly doubled in size over the past 24 hours. It went from 99 square miles to more than 165 square miles. Containment is only at 2 percent.
"Most of the fire activity is pushing to the east right into Yosemite," California Department of Forestry and Fire Protection spokesman Daniel Berlant said.
More than 2,000 fire personnel are fighting the blaze, named the "Rim Fire."
Within the park, the wildfire is burning in a remote area around Lake Eleanor and is not threatening Yosemite Valley, Bjorn Fredrickson, a fire spokesman for the U.S. Forest Service, said.
Yosemite remains open, but one of three entrances into the park on the west side, State Route 120, is closed.
Hundreds of people have been forced to evacuate from communities near the park. About 4,500 residences are threatened by flames.
Voluntary evacuation orders have also been issued for more than a thousand other homes, several organized camps and at least two campgrounds. The Strawberry Music Festival has been canceled.
The blaze began Saturday and has destroyed two homes and seven outbuildings. The cause of the fire has not been determined.
California Gov. Jerry Brown declared a state of emergency due to the huge fire, which frees up funds and firefighting resources.
The Associated Press contributed to this report.