Fisher, 60, went into cardiac arrest on the London to LA flight, the LA Times newspaper said.
Passengers attempted to revive her with CPR and she was taken to hospital when the plane landed after midday local time (20:00 GMT), the TMZ website said.
Her brother later told Associated Press she was in a stable condition.
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, celebrity news website TMZ reported. A medic who was travelling on the plane administered CPR.
Paramedics then spent a further 15 minutes administering more CPR to Fisher before getting a pulse, TMZ reported. The actress was on a ventilator in the UCLA medical centre, the website said.
United Airlines issued a statement saying that Flight 935 from London to Los Angeles 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 her condition was "not good".
Passengers on the plane have been tweeting about what they saw.
Fellow Star Wars actors have been posting messages of support.
Mark Hamill, who played Luke Skywalker, said he was sending all his love and Peter Mayhew, who played Chewbacca, tweeted his thoughts and prayers for "everyone's favourite princess".
Fisher appeared in the original Star Wars trilogy and Star Wars: The Force Awakens, a sequel released last year.
She also appeared in other films including The Blues Brothers and When Harry Met Sally.
She has written four novels and three memoirs and was previously married to the musician Paul Simon.
In her latest memoir, she revealed that she and Harrison Ford, who played Han Solo, had an affair during the filming of Star Wars when she was 19 years old, and he was 33 and married with two children.
She told People magazine: "It was so intense. It was Han and Leia during the week, and Carrie and Harrison during the weekend."
Fisher is the daughter of singer Eddie Fisher and actress Debbie Reynolds.
US actress Carrie Fisher, who played Princess Leia in the Star Wars films, has suffered a heart attack during a flight, reports say.