"Birthday wishes to the love of my life, the one person who showed me what passion truly was, the one that gave me solid morals to live by and how to dream," she wrote next to a picture of her father giving her a kiss.
The 19-year-old continued, "I will never feel love again the way i did with you. you are always with me and i am always with you. though i am not you, and you are not me, i know with all of my being that we are one. and our souls will never change in that way. thank you for the magic, forever and always."
The model and actress also posted a picture of herself at the MTV VMAs this past weekend with a photo-shopped image of Michael kissing her on the forehead.
Jackson died on June 25, 2009, at his home in Los Angeles.
Paris Jackson has been outspoken in the past about what a great father Michael was to her. In 2013, she spoke to The Daily Mail about the "normal childhood" she said Michael always wanted for his kids.
"I have lots of memories of my father," she said. "He was an incredible father. We all loved him to death."