Jasmine Magluyan was ripped from her mother's arms by a neighbor's dog. The girl was severely injured, but she is expected to survive.
The Great Dane named Zack has been put into quarantine for 10 days.
Police said the mother was holding Jasmine in her arms as she chatted with a neighbor when the dog suddenly appeared from inside the house.
"When they were over at the front door conversing with their neighbor, the neighbor's dog came up and snatched baby Jasmine out of the mother's hands and ran off down the street with the baby," said Capt. Jim Hunt of the Monrovia Police Department.
The dog ran about 100 yards with the baby in his jaws. The frantic mother and his owner chased him. He finally dropped the child and ran back home.
Jasmine was airlifted to Los Angeles County USC Medical Center where she was listed in guarded condition.
The baby's father said that the youngest of his three children suffered numerous injuries, including three broken ribs and a lacerated liver.
Police said the Great Dane is a licensed dog and has had his shots. Neighbors said the owners have two Great Danes.
"Investigation in the neighborhood has indicated so far that there's been no prior behavior that would've let anybody know that this would've occurred," said Hunt.
Officials said there likely will be a hearing to determine if the dog in quarantine will be deemed a vicious animal.