A man making a left turn at the intersection failed to yield and slammed right into them.
"He just came, made a left, and just took me and my kid," said Edgar Recinos, father of the child.
The 1-year-old boy, who was strapped in his stroller, flew about 25 feet before landing in the middle of the street.
The boy was rushed to a local hospital with multiple injuries, but he was expected to survive. He was released from the hospital early Thursday morning. Recinos also received minor injuries. The mother was not injured.
Because the boy was strapped into his stroller, he avoided more serious injuries.
"The only thing that really got messed up was the stroller," Recinos said.
The driver, believed to be an elderly man, was last seen traveling westbound on Saticoy Street.
Recinos said he believes the driver was a chauffeur and said he was wearing a uniform at the time.
The suspect's vehicle has been described as a black four-door Lincoln Town Car, with some minor damage from the accident.
Anyone with information is urged to call the LAPD at (877) LAPD-24-7.