Reynolds, 84, shared a message on Facebook on Tuesday morning, shortly after a family spokesman confirmed to ABC News that Fisher died.
The "Star Wars" actress was 60 years old.
"Thank you to everyone who has embraced the gifts and talents of my beloved and amazing daughter," Reynolds wrote. "I am grateful for your thoughts and prayers that are now guiding her to her next stop. Love Carrie's Mother"
Fisher was hospitalized on Friday after going into cardiac arrest on a trans-Atlantic flight to Los Angeles. Her brother, Todd Fisher, told ABC News at the time that she was in the intensive care unit and that the family was staying positive.
"We just need to tell everybody to keep the prayers up because the doctors are doing everything they can for her right now," he said. "She's a real survivor and always has been, and I would expect the best from this. That's how we're approaching it."
On Saturday, Reynolds wrote on her Facebook page that Fisher was "stable," although her medical condition was unclear.
"To all her friends and fans, I thank you all for your prayers and good wishes," she wrote.