Dennis Petillo, 24, was arrested shortly after the attack, which was reported at 12:51 a.m. at Van Nuys Boulevard and Sherman Way, officials said. He was being held in lieu of $500,000 bail.
Witness Erickson Ipina of North Hollywood told a camera crew he saw the suspect go into a nearby Walgreen's and buy what appeared to be rubbing alcohol.
"He just poured it all over the old lady, then he threw a match on her, and then started running," said Ipina, adding that the man threatened him with a knife.
Pina said he called 911, then followed the man until police arrived and arrested Petillo.
An ambulance and engine company from Fire Station 81 responded and transported the 67-year-old woman to a local hospital in critical condition, with burns all over her body, officials said.
Her identity was being withheld by authorities, but people in the neighborhood know her as Violet and said she'd been a regular at a local church.
'We've tried to get her off the bench for years, and she absolutely refuses. It was her home." neighbor Robert Wyneken told ABC7. "The people around here know her, and admire her, and love her."
The attack was being investigated by the fire department and detectives from the LAPD's elite Robbery Homicide Division, officials said.
The incident occurred eight days after a 55-year-old homeless man was set ablaze as he slept outside of a doughnut shot in Norwalk, officials said. He remains in serious condition at an area burn unit, officials said.
No suspect has been identifed in that attack.