It is the first completed ballot on the deal.
The TUI represents just under 15,000 second level teachers and lecturers.
Traditionally, if a majority of ICTU unions accept a deal like Croke Park, those who reject it abide by the majority vote.
However, the TUI executive has decided not to be bound by an overall vote in favour.
TUI President Gerard Craughwell said this could pose a huge problem for the Irish Congress of Trade Unions – particularly if other unions opposed to the Croke Park extension plans follow the TUI line and refuse to accept the majority vote.
The proposals in the Croke Park deal are aimed at reducing the public sector pay bill by an additional €1 billion over the next three years.