A Melbourne mother has been injured trying to fight off a greyhound after her one-year-old daughter was savagely attacked.

The girl's face was "ripped open" by a dog at a family home in on Raisell Road in Cranbourne West shortly after 9am today.

She was also bitten on the neck and shoulder, while her mother suffered lower body injuries attempting to fight the greyhound off.

Specialist paramedics treated the girl before she was rushed to the Royal Children's Hospital in a stable condition.

A baby has been attacked by a greyhound at a Melbourne property. (9News)

Her mother was taken to the Royal Melbourne Hospital.

The greyhound has been seized by City of Casey officers – who will now investigate the incident and determine whether the dog will be put down.

A man who arrived at the property shortly after the attack told 9News his greyhound was responsible.

Another greyhound was seen on the property behind a fence warning others to 'beware of the dog', (9NEWS)

He said it was being trained by a man at the home, but refused to comment any further.

Casey City Council Manager Safer Communities Caroline Bell said the attack was being investigated.