Costner had a special bond with Brown's mother, Whitney Houston, after their starring turns in 1992's "The Bodyguard."
"I was sad, obviously," Costner told People after hearing the news about Brown, 21, whose father is R&B singer Bobby Brown. "That family's under a lot of stress right now, just an enormous amount of stress."
"I can't imagine," Costner, 60, told People prior to receiving a career achievement award at the 14th annual AARP Movies for Grownups in Los Angeles on Monday.
"I really hope she's okay," said Costner, noting that it had been "a little while" since he's spoken with Brown.
On Monday, Brown's family released a statement revealing that she's "fighting for her life."
It's been almost three years since Houston was discovered in her bathtub at the Beverly Hilton. She died Feb. 11, 2012 at age 48.
Costner, who gave an emotional speech at Houston's funeral, recently opened up about the singer to CBS News, saying, "I had this unique window. I was right there. I held her hand. And I wasn't able to hold her hand after that. And I watched her journey. I watched the spiral. There was two or three times when I was asked to write her letters, that maybe this would have a level of impact on her. I wrote those letters. I never heard back. I was told that she got them. But she went away."