"I'm really worried about Redmond," the actress, 44, said Thursday. "I want them both to get better and get the help they need – especially my brother."
Tatum was herself arrested in New York on June 1 for trying to buy cocaine (she eventually pleaded guilty to disorderly conduct).
"[Addiction] runs in families. It's a disease," she adds. "I'm praying for both of them. I'm praying for my whole family. I hope Red will get treatment. That's what he needs. There is hope for Redmond. He deserves to have the life a [young man] – going to school, hanging out with friends, getting a job. I wish the best for him.”
Ryan O'Neal, 67, and his son, Redmond, 23, were arrested Wednesday at the actor's Malibu, Calif., home after substances believed to be methamphetamines were found.
"Deputies were doing a routine sweep to make sure Redmond was adhering to his probation," sheriff's spokesman Steve Whitmore said. "Upon searching the premises, the younger O'Neal was found in possession of narcotics. Later, a vial of drugs was found in the elder O'Neal's bedroom. We believe the drugs found were methamphetamines."
Hours later, Ryan and Redmond posted $10,000 bail each and were released from custody.
History of Drug AbuseRedmond O'Neal, whose mother is Farrah Fawcett, has a history of drug abuse, having entered rehab in 2004 for heroin use. This past June, he pleaded guilty to drug possession and one misdemeanor DUI charge.
Earlier Thursday, Tatum released a statement, saying, "Addiction, if untreated, can lead to jail, institutions and death. I love them both and I am sorry to hear about this."
Tatum O'Neal, who won an Oscar at age 10 for starring with her father in Paper Moon, told PEOPLE after her arrest in June that she hadn't spoken to her father in "years and years," and that her difficult childhood still haunted her.
After battling drugs and alcohol over the years, she said she had been sober a year when she was arrested. "I was trying to relapse," she said. "I made a giant, horrible mistake that I regret and feel really ashamed and embarrassed about. I take full responsibility."
She tells PEOPLE now,: "I'm sober. I thank God every day I have been able to overcome my demons and my stuff."
Tatum's family problems don't end with her father and half-brother. She is also concerned about her brother, Griffin's health. "He was diagnosed with melorheostosis, which is a rare bone disease,” she tells PEOPLE. “It's very rare. I'm worried about him, too."
For more information, go to: www.melorheostosis.org
Tatum opens up about her 'horrible mistake'
See ALL of Tatum's PEOPLE covers!
Stars battle their addictions on the covers of PEOPLE