They were allegedly subject to sexual abuse and forced to beg on the streets.
The owner, Rosa del Carmen Verduzco, and eight employees at the House of the Big Family have been arrested.
Correspondents say it is one of Mexico's worst incidents of alleged child abuse at a children's institution in many years.
'Utter dismay'
The government said the building was home to 278 boys, 174 girls and six infants under the age of three.
Map of Mexico
Also rescued were 138 adults aged up to 40, the government said.
Reports say the residents were forced to live in terrible conditions.
"I'm in utter dismay because we weren't expecting the conditions we found at the group home," local governor Salvador Jara said.
The House of the Big Family has been operating for 40 years and was known locally as Mama Rosa's Home.
The authorities began to investigate the home after parents complained that they were denied access to their children.
One woman, who grew up at the home herself, gave birth to two children who were registered in the name of Ms Verduzco.
When the mother left the home, aged 31, she was not allowed to take her children with her, investigators said.
String of allegations
Michoacan Governor Salvador Jara said the raid came after an official complaint was filed by the parents of five children who said they were being held at the home against their will.
Mr Jara said the complaint was filed more than a year ago. He did not say why the authorities had not acted sooner.
Local media had reported on allegations made against the home as far back as 2010.
An article in newspaper El Universal said six families had alleged that Ms Verduzco refused to hand over their children to them.
One mother told Universal reporters that she had taken her son to the home after a social worker had recommended it as a place for her child to get treatment for hyperactivity.
The mother, Martha Ines Lopez Ramirez, said she was only allowed to see her son once every four months and only ever in the presence of a "guard".
Ms Lopez said that her son seemed to have been drugged and showed signs of having been beaten.
'Abandoned children'
She told El Universal that all parents had been made to hand over custody of the children to Ms Verduzco, and sign a written agreement not to retrieve the children before they turned 18.
El Universal quoted Ms Verduzco at the time as saying that most of the children came from "dysfunctional families".
She told the reporters that the home was indeed "reluctant" to release children back to their families "unless the parents could demonstrate there had been an improvement in the family's condition".
A child welfare specialist consulted by the newspaper in 2010 said the allegations of mistreatment went back two decades but that Ms Verduzco was "politically well connected". bbc.com
