Miss Smith is a former members of the Irish Defence Forces.
She was not in custody for the four-and-a-half-hour journey but Irish police were waiting at Dublin airport for the plane's arrival.
"I think Lisa will actually be quite surprised by this turnaround, because when I interviewed her twice in Syria Lisa had no idea that there was any chance she could get arrested for this".
Her return was confirmed from a variety of sources, including those also onboard the commercial flight Smith and her daughter had seats booked on.
The Irish government has been working to repatriate Smith since her case was first reported by CNN in March.
Ireland's child and family agency as well as "different partners" are now looking into the "welfare of the child", he added.
She is being questioned at a Garda station in south Dublin under section 30 of the Offences Against the State Act.
On the Turkish Airlines flight back and while leaving the plane, Smith is said to have covered her face with a blanket.
Ms Smith has denied being involved in violence.
Irish Deputy Prime Minister Simon Coveney told Irish national broadcaster RTE on Sunday that authorities were working "primarily to ensure the safety of a 2-year-old girl who was in a warzone".
"They may be in a position to charge her and if they do, then a prosecution may follow".
As an Irish citizen she is free to return home to Ireland.
Dublin has said for months that it has a responsibility to find a way to bring Smith back to Ireland after she became aligned to the radical group in Syria and that its main concern was for the safe repatriation of her daughter.
"We've been given kind of indications that this might happen, but now it's been confirmed", she said.
So far Turkey has repatriated 10 German nationals, one United States citizen, and one British suspected fighter.