The incident unfolded around 5 p.m. Sunday on Hawthorn Avenue near La Brea, according to the Los Angeles Police Department.
Authorities say the 19-year-old man was arguing with the 48-year-old woman when he allegedly stabbed her several times.
She did not survive and the suspect fled the scene. Authorities later said the suspect was dating the victim's daughter.
A few hours later, police officers spotted him, which triggered a short pursuit. Authorities say he crashed into cars on the eastbound 10 Freeway. He was eventually arrested.
One woman in a car that he crashed into had an asthma attack, but no other injuries were reported.