The Wrecking Ball hitmaker claims in the papers that Kardalian sent her a letter when he was in prison saying he would turn up at her property when he was released.
When he did, he was intercepted by her security, and police were later said to have told him to leave.
Miley also alleges Kardalian has been using her address for his health insurance.
The pop star has enjoyed huge success in her music career, but recently said touring “isn’t healthy” for her.
The Flowers hitmaker - who released her latest album Endless Summer Vacation earlier this year - explained in a TikTok video: “Having every day the relationship between you and other humans being subject and observer isn’t healthy for me because it erases my humanity and my connection. And without my humanity and my connection, I can’t be a songwriter, which is my priority.”