Some 600 fire-fighters were battling the blaze that so far has burned some 1 500Ha, according to the Madera County Sheriff's Office.
With no containment in effect, the road allowing access to Yosemite from the south has been closed. However, the famous landmark remains open to the public.
As of Tuesday morning, some 1 000 people had been evacuated, with another 4 000 told they were now on standby, according to the sheriff's office. Shelters have been set up by the Red Cross for those who have to leave their homes.
At least eight structures have been damaged while at least 500 others risk being engulfed by the flames that were sparked early on Monday in the drought-hit, tinder-dry area.
The cause of the fire is under investigation.
In July, another inferno threatened a grove of famous giant sequoia trees in Yosemite, which welcomes several million visitors annually.
Last year, a gigantic blaze, the third largest in Californian history tore through a swath of the park, burning more than 10 926ha.