The star's security team held the woman and called police to the house, Los Angeles Police Sergeant Chris Coulter told the LA Times.
Bieber's security told officers the woman had tried to make contact with the singer three times in a week.
The woman was arrested and is being held on bail, Sgt Coulter said.
The woman - thought to be arrested on suspicion of trespass - is believed to be in her 40s.
The What Do You Mean singer was at home at the time of the incident, although the woman never managed to make contact with the star.