"A thorough review of this incident is under way," she added.
At least two investigations will be done, according to another corrections department statement.
The prison director commissioned a review team, to be made up of legal, medical, mental health, security and operational professionals not directly involved in the incident, to analyze Castro's death.
The Ohio State Highway Patrol will conduct a separate, independent investigation.
But Castro attorney Craig Weintraub said more precautions against a possible suicide should have been taken.
Castro's attorneys had requested permission for an independent forensic psychologist to evaluate their client, but were denied by officials, he said.
If Castro was believed to be suicidal, he should have been under stricter protection, he said.
Some will see his death as "a happy ending to this story, and a quick ending and justifiable," Weintraub said. "But we're in a civilized society and no one should really be celebrating this."
No place in the world
In handing down a sentence last month, Judge Michael Russo told the kidnapper there was no place in the world for his brand of criminal.
Castro pleaded guilty to 937 counts, including murder and kidnapping, in exchange for the death penalty being taken off the table.
The charges stem from his kidnapping, rape and assault of Knight, abducted in 2002; DeJesus, abducted in 2004; and Berry; abducted in 2003.
Castro is the father of Berry's 6-year-old daughter, DNA tests confirmed.
'You will die a little every day'
All three women kept diaries with Castro's permission, providing many of the details of their abuse.
"I cried every night. I was so alone. I worried what would happen to me and the other girls every day," Knight, 32, said, as she addressed her abductor head-on during his sentencing. "I will live on. You will die a little every day."
In each case, Castro lured the women into his car with the promise of a ride, according to court documents. The women and girl were freed in May after Berry shouted for help while Castro was away.
Neighbors heard her cries and came to her aid as she tried to break through a door. One neighbor gave her a cell phone to call authorities.
"Help me, I am Amanda Berry," she frantically told a 911 operator. "I've been kidnapped, and I've been missing for 10 years. And I'm here, I'm free now."
Plays the victim, blames the victims