A bus carrying pupils of Strabane Grammar School was attacked by Irish fans in the town centre on Wednesday.
It followed the World Cup match between the Irish Republic and Germany that ended in a 1-1 draw.
The school has told most pupils to stay at home during the next Irish game against Saudi Arabia on Tuesday.
West Tyrone assembly member Derek Hussey said children had been subjected to a barrage of abuse.
"The bus came under attack in the middle of the afternoon from people of all ages wearing Ireland colours and carrying tricolours.
"One window was smashed on the bus after a missile was thrown and, although no-one was injured, the pupils on board were traumatised and upset," he said.
'Appalled'
Mr Hussey said he had suggested to the FAI that Irish goalkeeper Shay Given, who is from nearby County Donegal, could intervene.
"I fully agree with the school that the safety of pupils is paramount and it is deplorable that such measures need to be enacted to ensure their safety because of a football match," he added.
The teachers' union, the NASUWT, which represents staff at the school, said it was appalled that it had been forced to close during any future World Cup matches played by the Republic of Ireland.
Regional official Tom McKee said: "The sectarian attacks by the Irish football fans on the school pupils are every bit as reprehensible as the sectarian invasion of the Belfast Institute building in east Belfast."