The warden, John Baird, told WOIO that a Chihuahua was found by police in Castro's car as he was arrested, and two other dogs that appear to be terrier-poodle mixes were found in his home.
The dogs appeared to be in good health, but needed heavy grooming, Baird told the station.
The FBI reportedly asked Baird to hold the dogs in case kidnapping victims Amanda Berry, 27, Gina DeJesus, 23, and Michelle Knight, 32, wanted the animals.
The three women disappeared between 2002 and 2004 when they were in their teens or early 20s. Prosecutors and police allege that Castro kept them captive in his home and beat and sexually abused them.