In a tweet, the Los Angeles County Sheriff's Department confirmed the shooting had occurred in the 11500 block of Dona Teresa Drive, but whether it was the suspect or a deputy who had opened fire was not immediately clear.
Four people were inside the house when investigators from the sheriff's West Hollywood station arrived with the warrant, officials said.
At a press conference near the house, a sheriff's spokesman was asked who had opened fire.
"At this time we don't know," Deputy Eric Ortiz told reporters. "There was deputies that were involved in the shooting but we don't know if it was the individuals at the residence or the deputies themselves."
Los Angeles Police Department officers were also seen at the location, which is in the LAPD's jurisdiction.
Aerial video from AIR7 HD showed authorities detaining a man at gunpoint outside the home, but whether he was a suspect was unknown.