The 60-year-old actress, who played Princess Leia in the Star Wars movies, went into cardiac arrest minutes before the end of the flight.
According to TMZ, passengers attempted to revive Carrie Fisher with CPR and she was taken to hospital when the plane landed after midday local time.
Todd Fisher said she was in intensive care in LA.
He told Entertainment Tonight: “If everyone could just pray for her that would be good.
“The doctors are doing their thing and we don’t want to bug them. We are waiting by patiently.”
Carrie Fisher had been on tour promoting her latest book, The Princess Diarist.
The heart attack happened about 15 minutes before the plane landed in LA, TMZ reported. A medic who was travelling on the plane administered CPR.
Paramedics then spent a further 15 minutes administering more CPR to Carrie Fisher before getting a pulse, TMZ reported. She was on a ventilator in the UCLA medical center, the website said.
United Airlines issued a statement saying that Flight 935 from London to LA was met on the ground by medical personnel after the crew reported that a passenger was “unresponsive”, but did not name the passenger, Reuters reported.
The LA Fire department said its paramedics met the plane and “provided advanced life support and aggressively treated and transported the patient to a local hospital”.
A law enforcement official told NBC that Carrie Fisher’s condition was “not good”.
Carrie Fisher appeared in the original Star Wars trilogy and Star Wars: The Force Awakens, a sequel released in 2015.
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