It was claimed the remark came at a prize-giving ceremony at the Palace of Holyroodhouse for his Duke of Edinburgh award.
After a winner said he had worked in Romania, the Duke reportedly replied: "Romania? You didn't go across to help in one of those orphanages, did you?"
When the student said no, it was claimed the 85-year-old duke added: "Ah good, there's so many over there you feel they breed them just to put in orphanages."
More than 47,000 youngsters were abandoned by poverty-hit parents in Romania in 1991 after the fall of President Ceausescu.
Tony Allen, of the Romanian Orphans Appeal, labelled the duke's comment "disgusting".