Ms Ruane said it was gutter journalism and a “dreadful attack” on her family.
She said she paid for her daughter to go with her and private matters should not be brought into “political battles”.
“I will make decisions in relation to my family,” she said. “I’m a mother and I’m a minister.”
Ms Ruane said she was in Cyprus on official business, speaking about the peace process and education in Ireland “and the lessons that Cyprus can learn”.
In a later statement she added: “My decision was dictated by private and personal matters and in the best interest of my daughter.
“I am happy that my decision was both responsible and correct.”
Mervyn Storey, who chairs the education committee at the Northern Ireland Assembly, criticised Ms Ruane.
“I think this is another example of how the minister sets a standard for others, but is not prepared to live by the rules herself.”
Basil McCrea, the Ulster Unionist education spokesman, said as minister, Ms Ruane advised other parents not to take their children out of school during term time.
“There is an issue for people in public life that if you do one thing and say another, it worries people.”
However, Brendan Harron, from the INTO, said each decision must be judged on merit.
“Attendance at school is crucial – there’s a clear link between attendance and achievement – but every individual case must be looked at on its merits,” he said.
“A parent makes a decision – I don’t think any parent makes a decision to in any way inflict damage on a child’s education.”