Paramedics went to the 32-year-old actor's Malibu home early Wednesday morning when someone called saying he had suffered a stroke.
Sheen was in stable condition Thursday in the critical care unit at Los Robles Regional Medical Center, said Chris Caraway, a hospital spokeswoman.
Doctors were awaiting results of blood tests to determine what drug the star of Wall Street and Platoon took, though hospital officials confirmed he was being treated for an overdose.
During a press conference held Thursday night, his father, actor Martin Sheen, spoke to reporters.
"We are in the stages, right now, of recovery. It is my hope that he will accept recovery and become free. I am asking all of his friends and fans to pray for him," Sheen said, his wife, Janet, at his side.
The elder Sheen said he was helped by fellow actor Carroll O'Connor, who starred in the '70s TV sitcom All in the Family, and the messages he tried to get across after losing his son, Hugh. Several years ago, Hugh committed suicide because of a chronic drug problem.
"I am very motivated by our dear friend, Carroll O'Connor. I'm very much appreciative of the messages that he took the time to record after ... he lost his son," Sheen said, choking back tears. "And they've been clear about ... do anything you can to get between the drugs and your kids. And that's what I'm doing."
Los Angeles County paramedics rushed Charlie Sheen, accompanied by his personal trainer, to the hospital. He was admitted early Wednesday, conscious but complaining of tingling in his hands and difficulty walking.
Charlie Sheen has a troubled past dating to 1990, when he checked himself into a drug and alcohol rehabilitation facility.
In 1995, a woman sued him, alleging that he struck her in the head several times when she refused to have sex with him.
He admitted in videotaped testimony at the 1995 federal trial of Hollywood madam Heidi Fleiss that he ordered her call girls at least 27 times, running up a tab of more than $50,000.
In early 1996, Sheen announced that he planned to divorce model Donna Peele after less than six months of marriage.
Later that year, Sheen announced he was a born-again Christian and that fast living "was a lot of fun, but there is such a thing as too much fun ... It gets redundant. How many times can you wake up and struggle to remember your name, her name, and where you are?"