In a post on Twitter, the ministry said the three, including two children, had been caught trying to illegally enter the country.
One of them, a 26-year-old woman, identified by the initials S. A., is described as a terrorist belonging to Islamic State.
The Turkish Ministry of National Defence said she was wanted with a "blue notice" - an international request from Interpol for countries to share information regarding her identity, location, and activities in relation to a crime.
New Zealand's Ministry of Foreign Affairs and Trade said it was aware of the information.
Waikato University international law expert Al Gillespie said thousands of westerners were still in that region having travelled there in 2014 onward, and many were in refugee camps or had tried to make their way home.
"We don't really know the numbers that were over there of Kiwi nationality, but these ones have turned up and now we have to decide what to do next," he told Morning Report.
"The fighters is one thing, but the brides and the children is another, and this decision over whether you help bring people back has split most western countries.
"Some will have nothing to do with anyone who went to fight in the conflict. Other countries have said we'll look at this on a case by case basis and we'll help bring back the women and the children because they weren't at the forefront of the conflict."
All New Zealanders have a right to come back to the country but that did not mean the country had to facilitate their return or pay for them to come home, he said.
"You can argue that our responsibility foremost is first to the children, then to the non-combatant and then lastly to the combatant".
"The problem is more complicated because New Zealand is a very difficult county to get into full stop right now, so trying to argue that anyone should be advanced through that waiting list is a no gamer."
