The parents, 57-year-old David Allen Turpin and 49-year-old Louise Anna Turpin, couldn't give a good reason as to why their children were restrained, the sheriff's department said.
They were ordered held on $9m bail each and are due to appear in court on Thursday.
However, they said their officers found the siblings, aged between 2 and 29, in a foul-smelling house.
United States police said the 13 siblings range in age from 2 to 29 and that some were found shackled to beds. They appeared malnourished and dirty, and told authorities they were starving.
The discovery was made, after one of the captives managed to break free and call 911 from a cell phone she discovered inside the house.
Kimberly Milligan, 50, who lives across the street from the family, said she only saw the infant in the mother's arms and three other children since she moved in across the street two years ago, describing them as small and pale.
The 13 children have now been admitted to a local hospital and once they are discharged, they will be under the care of the Child Protective Services and Adult Protective Services.
Records say the school was opened in March, 2011. Authorities conducted a short interview with the girl, then they contacted the parents at the home where she had escaped, the release stated.
"They're very friendly", he said. No movement, like if they were told not to speak to anybody.
She did not recall hearing about a school run from their home.More news: Trump denies saying he probably had good relationship with Kim
"I thought the kids were home-schooled", she said. I haven't seen her in 19 years.
The couple's neighborhood is a new development of ranch-style homes located about 70 miles east of Los Angeles.
The California Department of Education said in a statement, "We are sickened by this tragedy and relieved the children are now safe and authorities are investigating".
Mr Turpin senior said all 13 children were his son's biological offspring and none were adopted. She frequently wondered why the many children never came outside to play.
One neighbour told the Press Enterprise: 'I didn't know there were kids in the house. If you've been deprived of normal childhood activities, normal interactions and the people who should have been providing for you have failed to do so, that is going to cause some psychological damage.
David's parents James and Betty Turpin told ABC News that they were "surprised and shocked".
Neighbours said the Turpins rarely emerged from their home.
On Facebook, the children appear to happily pose for photographs in matching clothes on trips to Disneyland and to Las Vegas.
They are surrounded by the 13 siblings, all smiling.