Authorities say the man, who is in his 20s, was arrested early Thursday. His name was not immediately released.
Police say the attack occurred shortly after 1 a.m. outside a drug store. A witness said he saw a man come out of the store and pour something on the woman before striking a match and setting her ablaze.
The woman, who may be homeless, was taken to a hospital and listed in critical condition.
Last week, a 55-year-old man was set on fire as he slept outside a doughnut shop in southern Los Angeles County. No one has been arrested.
