Bobbi Kristina Brown, 21, is in a medically induced coma after being discovered in her home in the US state of Georgie.
Almost three years ago her mother Whitney was found dead in similar circumstances.
Costner, who stared alongside Whitney in the film Bodyguard, said the family was "under a lot of stress right now, just an enormous amount of stress".
He added that he was praying and watching like everybody else.
A statement from the family read: "Bobbi Kristina is fighting for her life and is surrounded by immediate family.
"As her father already stated, we are asking you to honour our request for privacy during this difficult time.
"Thank you for your prayers, well wishes, and we greatly appreciate your continued support."