The carcass was discovered at about 7:30 a.m. in the 200 block of Portola Road, near Woodside Priory School.
Emergency officials said there were tracks nearby that may have been left by a mountain lion.
There have been a number of mountain lion sightings in the Woodside and Portola Valley areas in the past few weeks, but wildlife officials say the cats generally avoid confrontations with humans.
However, county officials advise residents to keep an eye on small children and avoid jogging or hiking at dawn, dusk, and at night when mountain lions tend to roam around.
In the event of a mountain lion encounter, wildlife officials advise residents to face the animal, make noise and try to appear as large as possible.
Visit keepmewild.org for information on mountain lions from the California Department of Fish and Game.