Fisher, 60, who played Princess Leia in Star Wars, was taken ill on a flight from London to LA on Friday.
Passengers attempted to revive her with CPR and she was taken to hospital when the plane landed.
Co-star Harrison Ford said he was "shocked and saddened" by the news.
"Our thoughts are with Carrie, her family and friends," he said. Ford played Fisher's on-screen love interest in the franchise, and Fisher revealed earlier this year in a memoir that the pair had a brief off-screen romance.
Mark Hamill, who played Luke Skywalker, said he was sending "all our love" and Peter Mayhew, who played Chewbacca, tweeted his thoughts and prayers for "everyone's favourite princess".
Fisher's brother Todd said she was in intensive care in Los Angeles. "We have to wait and be patient," he said. "We have so little information ourselves."
He added: "She's obviously a very tough girl who's survived many things. I encourage everyone to pray for her."
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 said. The actress was on a ventilator in the UCLA medical centre, the website said.
A law enforcement official told NBC that her condition was "not good".
Passengers on the plane have been tweeting about what they saw.
Fisher appeared in the original Star Wars trilogy and Star Wars: The Force Awakens, a sequel released last year.
She was 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.
She is the daughter of singer Eddie Fisher and actress Debbie Reynolds.
Friends, family and colleagues have sent best wishes to the actress Carrie Fisher, who is in intensive care after suffering a heart attack during a flight, her brother says.