Witnesses reported hearing more than five shots in the 6100 block of Hollywood Boulevard, about two blocks east of Vine Street.
Dozens of people had gathered at the singer's star on the Hollywood Walk of Fame to honor his memory. The 81-year-old performer died on Sunday in Mexico.
Mexican singer Vicente Fernández dies at 81
Witnesses tell Eyewitness News they saw what appeared to be a person's arm holding a handgun fire into the air from an upper-story apartment across the street from the memorial.
At least one bullet struck a glass door on the same side of the street where people had gathered for the memorial.
There were no injuries reported. It was not clear if the shots were intentionally aimed at people gathered on the Walk of Fame.
LAPD officers responded to the scene very quickly. They began searching the area and cleared the crowd out from the memorial to establish a crime scene.
By around 8 p.m., the LAPD confirmed that officers had taken a man into custody in connection with the shooting. His identity was not released. His motive and target remain under investigation.