Ashley Newton, 23, of San Jose was arrested Saturday on suspicion of murder, the East Bay Regional Parks District Police Department said in a statement.
Investigators continue to interview her family and friends in an attempt to make sense of the alleged crime.
"This is an extremely shocking case for us," said Chief Timothy Anderson of the park's police department.
The motive remains unclear, but Anderson said that Newton had a history of depression and appeared to have self-inflicted knife wounds on her wrist.
Police were called at 10:30 a.m. Saturday on reports of a damaged Honda sedan in the Del Valle Regional Park east of San Francisco. They found the car abandoned with the engine running and an empty child's seat.
Officers were about to tow the car two hours later, believing it was involved in a hit-and-run, when Newton walked up to them holding her lifeless baby, Anderson said.
Officers tried to resuscitate the baby, but he was pronounced dead at the scene.
Newton was arrested after she made statements implicating herself in the stabbing, Anderson said, adding that investigators found a knife in the area that they believe was used in the alleged crime.
The stabbing occurred in a remote part of Camp Arroyo, the site of a popular children's camp inside the 4,400-acre park south of Livermore, a suburb that's about 45 miles east of San Francisco.
Newton remains in jail with no possibility of release on bond, police said.
She is due in court on Tuesday.