The 21-year-old, who is the daughter of the late Whitney Houston and singer Bobby Brown, was found unresponsive in a bathtub at her home in Atlanta on Saturday.
She is currently at North Fulton Hospital in Georgia, and has been placed in a medically induced coma.
In a statement, her family said: “Bobbi Kristina is fighting for her life and is surrounded by immediate family.
“We are asking you to honour our request for privacy during this difficult time.”
Superstar Whitney died in similar circumstances in 2012, aged 48, when she drowned in a bathtub due to cocaine use and heart disease.
According to reports, police have confirmed that no drugs were found at Bobbi’s home.
Lisa Holland, of the Roswell Police Department, said: “There were nothing there that indicated that anything out of the ordinary happened. There were no drugs out in the open.”
In a previous statement, 45-year-old Bobby said: “Privacy is requested in this matter. Please allow for my family to deal with this matter and give my daughter the love and support she needs at this time.
Family members allegedly insisted Bobbi was finally getting her life back on track following her mother’s death three years ago.