Judge Lisa Gorcycae held the children in contempt of court, saying they would be detained throughout the summer.
She said the children, aged between nine and 14, had been “brainwashed” by their mother, according to NBC News.
Their parents have been involved in a bitter divorce and custody battle since 2009.
The Oakland County judge said the two boys and one girl can see their father, Omer Tsimhoni, while detained but not their mother, Maya Eibschitz-Tsimhoni.
Mr Tsimhoni is a traffic expert who works for General Motors, while Ms Eibschitz-Tsimhoni is a pediatric doctor.
Judge Gorcycae was reported to have told the family that it was one of the worst “parental alienation” cases that she has seen.
It is unclear how long they will be detained for.
The 24 June ruling, which only came to light this week when court documents were released, was made after the children refused the judge’s order to go for lunch with Mr Tsimhoni.
Ms Gorcycae said the children had disobeyed her orders to “have a healthy relationship” with their father.
One of the boys told the judge that his father had been violent towards his mother, but the judge told the children: “Your dad is a good man who loves you. You have been brainwashed.”
Mr Tsimhoni’s lawyer also blamed the children’s mother for “alienating” the children from their father.
The lawyer for Ms Eibschitz-Tsimhoni has not commented on the children’s detention.
The children are being kept at a centre in Pontiac, northwest of Detroit, called Children’s Village, where as many as 200 juvenile offenders are held.