The Alameda County Sheriff's Office told the San Jose Mercury News that the woman and her daughter went alone to the Del Valle Regional Park in the afternoon. The 41,000-acre park is 10 miles south of Livermore, about 45 miles east of San Francisco.
It was unclear when the stabbing happened or what type of weapon was used. The crime scene is near the Arroyo Dam and the Wente Golf Course.
Deputies told the newspaper that the woman is being held with no possibility of release on bail.
The woman's name was not immediately released, and deputies said they didn't know what may have led the woman to lash out.
The park remained open to the public as deputies investigated.
