The emotional scene can be seen in a preview trailer for the chat show queen's upcoming interview with the 18-year-old.
It will be the first time the teenager has spoken since her mother's death.
In the interview, which will be screened on her OWN network in the US on Sunday, Bobby shares personal memories of her mum.
Oprah also speaks to Whitney's sister-in-law and manager Patricia, and brother Gary, and addresses the rumours and speculation surrounding the singer's death.
Whitney and Oprah were friends and the TV boss attended the Saving All My Love For You singer's funeral last month.
The 58-year-old host is also close to Bobbi, who – according to TMZ – has been singing her praises.
"[Oprah] was loyal to my mum, and never did my mother wrong, or made her look bad. She always looked out for my mum," the website quotes her as saying.