The flight was on approach to Los Angeles when the 60-year-old actress who played Princess Leia in "Star Wars" became ill.
Fisher was transported to a hospital from Los Angeles International Airport, the source said.
"Carrie Fisher is still in the ICU," Todd Fisher, the actress's brother, told CNN by phone Friday evening.
The Los Angeles Fire Department previously said it responded to a cardiac arrest at the United Airlines gate where the London flight arrived.
