Ashley Newton, 23, of San Jose was arrested Saturday, according to the East Bay Regional Parks District Police Department.
Police responded to reports of a damaged Honda sedan in the park and found the car abandoned with the engine running and an empty child's seat.
As officers were preparing to tow the car, Newton walked up to them holding her lifeless baby.
She was placed under arrested after investigators say she implicated herself in the stabbing. A knife believed to have been used in the crime was found nearby.
The motive remains unclear, but Newtown allegedly has a history of depression and appeared to have self-inflicted knife wounds on her wrist.
Newton remains in jail with no possibility of release on bond. She is due in court on Monday.
The Associated Press contributed to this report.