Police said officers thought the man had a gun, but he turned out to be unarmed.
The man flagged down officers about 6:35 p.m. at Los Feliz Boulevard and Tica Drive south of Griffith Park, according to a police account.
"This person extended an arm wrapped in a towel. The officer exited the vehicle and said, 'Drop the gun, drop the gun,'" LAPD Lt. John Jenal said.
Then at least one officer shot the man, officials say. He was taken to a hospital where he was listed in critical condition.
A motorist shot graphic video of the officers handcuffing the man with a visible head injury.
LAPD Cmdr. Andrew Smith, a department spokesman, said the officers followed standard procedure in handcuffing the man when they did. At that point, Smith said, the man had not been searched and was considered a suspect.
"We always do that," Smith said. "That's the policy ... to handcuff someone in a situation like that."
Smith cautioned that the investigation into Friday's shooting was still in its early stages. One of the key questions, he said, was why the man flagged down the two uniformed officers.
The man was standing on the side of the road, Smith said, when he called out to the officers: "Police, police."
Smith said investigators would explore all possibilities, including whether the man needed some type of help from police. He said investigators would also look into the man's background to see if there were any indications the shooting was an attempted "suicide by cop."
The man's name has not been released.
"We cover everything. Our investigators leave no stone unturned," Smith said. "We don't have any idea about this guy's background. We just don't know yet."
The shooting in Los Feliz was one of two Friday in which LAPD officers shot a man who was partially concealed by a blanket or towel. Earlier in the day, LAPD officials said, officers wounded a man in El Monte after he got out of a car covered in a blanket and then brandished a gun. The man, who was critically wounded, had led officers on a two-hour chase that began in South L.A. after he allegedly assaulted a woman.
Smith said investigators would also examine whether the officers involved in the Los Feliz shooting were aware of the other incident earlier in the day.
The officers in the Los Feliz shooting were assigned to the LAPD's Security Services division — a detail that typically provides security at city facilities, Smith said.
Except for a small strip of yellow police tape tied to a porch railing, there were no signs Saturday morning that a shooting had occurred in the Los Feliz neighborhood. The shooting happened along a stretch of Los Feliz Boulevard popular among joggers and people walking their dogs, not far from a stretch of restaurants drawing their typical weekend brunch crowds.
Kelsey Magnuson, 31, has lived in the building across the street from where the shooting occurred for almost 10 years. She said she was surprised when she learned of the shooting Friday, given how safe the area feels.
It's the kind of neighborhood where someone can step outside their building for a late-night cigarette and not feel threatened, she said.
"I've never felt like there would be anything worrisome here," she said. "It makes you wonder what the commotion was."
The Los Feliz shooting marks the latest of several high-profile police shootings the LAPD is grappling with.
Last week, the Los Angeles Police Commission concluded that one of the two L.A. police officers who fatally shot Ezell Ford, a mentally ill black man, last summer was not justified in using deadly force.
LAPD reports found that Ford and the officer were struggling over the officer's weapon. But the commission decided that the officer did not have a reason to stop and detain Ford in the first place. His handling of the encounter, the commission concluded, was so flawed that it led to the fatal confrontation.
The LAPD is also investigating the fatal police shooting of an unarmed and homeless black man near the Venice boardwalk in May.
L.A. police Chief Charlie Beck has said he was "very concerned" about the May shooting. "Any time an unarmed person is shot by a Los Angeles police officer, it takes extraordinary circumstances to justify that," Beck told reporters in May. "I have not seen those extraordinary circumstances."
The LAPD is now investigating the Los Feliz shooting. Based on the video, the officers and the injured man all appear to be white.