The incident occurred on the 500 block of Rayen Street on May 1.
Police say the suspect was sitting in the upper stairwell when the victims entered the apartment complex. When the victim opened her apartment door, the suspect grabbed the little girl's arm and held a large knife to the mother's stomach.
Detectives say the suspect spoke Spanish and demanded money from the victim. The mother who had just came home from the bank complied and handed over several hundred dollars. The suspect then fled eastbound on Rayen Street.
Investigators believe the man was trying to intimidate the woman.
"When you commit a crime that significant where you grab a small child, in this case, we're talking about a 3-year-old and you hold a knife to the woman's stomach, this is a dangerous individual," said LAPD Det. Thomas Barnhart.
The victim reported the crime immediately. The composite sketch, however, took some time to develop.
The suspect was described as a Hispanic man with brown or grey hair standing 5 feet 8 inches tall and weighing around 170 pounds. He is believed to be around 45 years old with black or grey facial hair.
The LAPD released a sketch of the suspect in hopes the public will recognize the man and lead authorities to his arrest.
"We don't know what his motives were," said Barnhart. "We don't know if he targeted her but our hopes are that somebody will help us identify him so that we can get him off the streets."
Police say the victim does not know the suspect.
Anyone with any information regarding the suspect or his whereabouts was urged to contact LAPD's Mission Division at (818) 838-9800.