The baby goat was among a small herd of goats that became trapped between the flames and a fence last Thursday.
VIDEO: Goats flee fast-moving grass fire in Milpitas
VIDEO: Goats flee brush fire in Milpitas
Most managed to escape with minor burns, but the young female's injuries were much more significant.
The shelter manager for Animal Care and Services in San Jose said all the other goats have been placed in either farm sanctuaries or taken by private citizens known to be responsible, and knowledgeable people who will provide the appropriate care for the goats.
San Jose Animal Services cared for at least 10 of the 15 goats after the fire. Their injuries included first, second and third-degree burns.
VIDEO: Goats survive grass fire in Milpitas
Perhaps the best indication of how much they suffered was how quiet they were after the fire. "They do have emotions, so I'm sure they are traumatized. They lost their home, they had to run for their lives," shelter spokesperson Julie St. Gregory said.
The injured goats were surrendered by the Milpitas property owner after the fire. He kept five goats that did not appear to be injured.
The shelter is seeking donations to help pay for the expenses, while they took care of the goats.
Click here to make a donation to help the shelter.