Video shows the newborn being taken by a woman who was in a silver or gray 2016 Ford Focus hatchback. She is seen casually walking back to the car's passenger side, with the goat under her arm.
Owner Terry Oyarzun said the baby needs to be back with its mother in order to survive.
"The goat mama just wants her baby back," said Oyarzun. "They're nice little family animals, and she's sad. And the baby goat really needs the mom. She needs the mom's milk to be able to thrive."
Anyone with information should call Pinole police.