Ashley Newton, 23, was scheduled to be arraigned in Alameda County Superior Court in Pleasanton at 2 p.m. for the death of her son, William Brian Sherman.
East Bay Regional Park District police said they received a call reporting a traffic collision at about 10:30 a.m. Saturday on Arroyo Road near the Wente Vineyards.
Officers who responded to the scene found a badly damaged 2013 Honda sedan that was abandoned on the roadway near the park district's Camp Arroyo facility.
East Bay Regional Park police Sgt. Tracy Desiderio wrote in a probable cause statement that, "Newton appeared in the roadway holding a lifeless baby in her arms."
Witnesses immediately began emergency medical aid and summoned medical professionals, but the boy was pronounced dead at the scene, Desiderio said.
Newton "made several spontaneous statements indicating that she had killed the baby," Desiderio said in her statement.
After officers read Newton her legal rights, she "again admitted to stabbing the baby numerous times," Desiderio said.
At one point, Newton said, "I'm sorry, I killed my baby," Desiderio wrote.
In addition to murder, Newton is charged with an enhancement clause of using a deadly weapon, namely a knife.
Park district police said a knife they believe Newton used was found at the scene.
Authorities said Newton had an apparently self-inflicted stab wound to her wrist and was treated at a nearby hospital before being taken into custody.
Park district police said Newton had a history of depression but they are still trying to determine a motive for the fatal stabbing.