The armed suspect entered an apartment in the 200 block of Playa del Rey around 10:30 p.m. and confronted the 18- and 19-year-old women, police spokeswoman Margo Rohrbacher said.
One of the women called police during a physical fight between the suspect and the other woman, Rohrbacher said.
The woman suffered a minor injury and was treated by a paramedic.
The suspect was wearing a black hooded sweatshirt and only his face was exposed, Rohrbacher said.
He fled before police arrived, but he received substantial facial injuries and possible stab wounds to the upper body and may have sought medical attention, Rohrbacher said.
The women were able to provide a good description of the suspect, and police hope to release a sketch of him soon, Rohrbacher said.
Police asked all hospital emergency rooms and clinics in the Bay Area to alert them if they receive a patient matching the suspect's description, Rohrbacher said.
The suspect is 19 to 25 years old, 5 feet 6 inches with a thin build. He has dark skin, high cheekbones and "sun spots" on his face, Rohrbacher said.
Police canvassed homes in the area for more witnesses this afternoon, and are checking on parolees, probationers and registered sex offenders, Rohrbacher said.
Evidence at the scene will be sent to the Department of Justice for analysis, Rohrbacher said.
Anyone with information is asked to call police at (415) 485-3000 or Crime Stoppers at (800) 222-8477.