After the plane landed at Los Angeles International Airport on Friday, the Los Angeles Fire Department responded and administered CPR prior to transporting the actress to UCLA Medical Center.
Todd Fisher told Eyewitness News that his sister is "getting the best care she can receive."
"She's obviously a very tough girl who's survived many things," he said in an interview.
"I encourage everyone to pray for her."
Carrie and Todd Fisher are the children of entertainers Debbie Reynolds and the late Eddie Fisher.
as if 2016 couldn't get any worse... sending all our love to @carrieffisher— Mark Hamill (@HamillHimself) December 23, 2016
United Airlines released the following statement:
Medical personnel met United flight 935 from London to Los Angeles upon arrival today after the crew reported that a passenger was unresponsive. Our thoughts are with our customer at this time and any requests for additional information should be directed to local authorities.
MORE: Celebrities share thoughts, prayers for Carrie Fisher following cardiac arrest
The 60-year-old actress is best known for her role as Princess Leia in the classic film series, "Star Wars," the first of which was released in 1977.
Fisher reprised that role in the 2015 film "Star Wars: The Force Awakens."
Fisher has authored several books and had been touring to promote her latest work, "The Princess Diarist," which made headlines when it was released in November for its disclosure that she had an affair with then-married actor Harrison Ford during filming of the original "Star Wars."
MORE: Carrie Fisher describes "Star Wars" filming in rare 1977 interview
The actress was briefly married to singer Paul Simon in the 1980s. She has a 24-year-old daughter, Billie Catherine Lourd, fathered by talent agent Bryan Lourd.
Fisher has openly discussed her problems with cocaine and prescription medication abuse, memorialized in her memoir, "Wishful Drinking," which was adapted from her one-woman stage play of the same name.
In addition to "Star Wars," Fisher has appeared in films including "The Blues Brothers," "The Man with One Red Shoe," "Hannah and Her Sisters," "The 'Burbs," "When Harry Met Sally," "Charlie's Angels: Full Throttle" and "Fanboys."
She also wrote the semi-autobiographical novel and screenplay for the film "Postcards from the Edge."
City News Service contributed to this report.