A person was also shot by a police officer during the stabbing spree near Skid Row in downtown LA.
The condition of the victims is currently unknown.
The LAPD said that no officers were hurt in the incident.
Police at the scene of the stabbings in Los Angeles
The shooting occured shortly before noon near San Pedro Street south of 6th Street. That's also where one of the stabbing victims were found, treated and transported to a local hospital.
Two other victims were also found – one near San Julian Street south of 6th Street and Crocker Street north of 6th Street.
Police at the scene after a mass stabbing near Skid Row in LA
Officer Lilian Preciado said that one person was taken into custody in connection with the incident.
LAPD’s Central Division is on tactical alert, officials said.
According to one local media report a person has been arrested in connection with events.
Deputy Chef Robert Arcos, who heads the LAPD's Central Bureacu said witnesses reported seeing a person stab at least three people in three different locations in skid row.
Officers on one of the LAPD’s RESET teams — which focus on skid row — responded to the area and saw the suspect, Arcos said.
During that incident police shot the suspect.
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Police attend the scene in downtown Los Angeles
The suspect was taken to a hospital in unknown condition, Arcos said.
Police had blocked off San Pedro between 6th and 7th in front of the Midnight Mission, where a witness said he saw two men fighting shortly before the shooting.
The man, who asked to be identified only by his first name of Riccolo, said two men began arguing around 12.05pm local time.
Riccolo said he did not know the men or what they were fighting about, and could not see a weapon.
Riccolo said he saw officers fire five shots at the man.
He said: “They positioned themselves and fired until the body stopped moving."
The area where police had established a crime scene is lined with tents and a small crowd had gathered at the edge of the perimeter, some of whom bemoaned another shooting on Skid Row.