The incident was reported around 4:30 a.m. in the 9700 block of Longden Avenue, the Los Angeles County Sheriff's Department said.
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Investigators say a man came home after a night out with friend and found two armed robbers in his home. Two women in the home had been zip-tied. A baby was also in the home but was not harmed.
The occupants of the home had been sleeping when the robbers broke in, likely through a side window or door, investigators say.
When the man arrived home, there was a struggle and he was shot in the elbow. The two thieves ran off with about $2,000 cash from the man's pocket. His friend drove him to a local hospital.
Descriptions of the perpetrators were not immediately available.
There is no indication the robbers knew the victims.
The situation has residents in this community terrified.
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"I almost cried," said one neighbor, who identified herself as Lisa T. "I almost cried for the family. So sad."
Officials say there have been other robberies in the area. They had some basic advice for people to keep safe:
"Lock their doors, pay attention," said Det. Richard Lewis with the LASD. "Have cameras that work, not just as window dressing."
Investigators urged anyone with information about the crime to call the sheriff's Temple station at (626) 285-7171.