Cyrus, 19, was out of town at the time of the incident. Police said they received an emergency call from the property after the man got onto the grounds before dawn on Saturday, knocked on the door and banged on the walls of the former "Hannah Montana" star's house.
Los Angeles police said officers found the man hiding in the bushes and jailed him for trespassing. He was carrying scissors in a back pocket.
Celebrity news website TMZ.com ran video of the arrest, in which the man is heard telling police as they searched him: "I am a friend of Miley Cyrus. I am. She's my wife. Me and Miley have been friends for five years."
Cyrus rose to fame as the star of the Disney Channel's "Hannah Montana" show. Cyrus went on to build a worldwide singing career that includes hits like "Party in the U.S.A." and "The Climb."