The 21-year-old's husband and a friend found her non-responsive in the bathtub of her home near Atlanta, Georgia on Saturday (January 31) in an incident with eerie echoes of her mother's drowning in a Los Angeles tub in 2012.
"Bobbi Kristina is fighting for her life and is surrounded by immediate family," the Houston family said in a statement provided to US media.
There has been no official word of Brown's condition, but several US media outlets including CNN and the TMZ.com entertainment news site have cited family sources as saying she was in a medically induced coma.
"We are asking you to honor our request for privacy during this difficult time," the family statement added.
"Thank you for your prayers, well wishes, and we greatly appreciate your continued support."
Whitney Houston died in February 2012 when she was found in a bathtub at the Beverly Hilton Hotel in Los Angeles on the eve of the music industry's annual Grammy Awards show.
Coroners concluded she died by accidental drowning, with cocaine use and heart disease as contributing factors.