Leigh Church of England Junior School in Greater Manchester is being looked into by Wigan Council and Greater Manchester Police following claims that children had been made to stand in the cupboard.
Chairman of governors at the school David Sanderson said that he wanted to reassure parents that they were taking the allegations "very seriously".
He said: "Parents may have been made aware of media reports relating to an issue of safeguarding at the school. We take any allegations of this nature very seriously and an investigation has been launched into the concerns raised."
One parent whose 11-year-old son was allegedly banished to the cupboard said she had been contacted by a social worker regarding the incident.
Victoria Francis said that she had been "disgusted" to learn that her son Nathan, who has dyspraxia, had been left for more than an hour.
She told the Manchester Evening News: "Nathan suffers from dyspraxia and told me he was put in there for not writing as quickly as the rest of his class. To be punished for having a disability is despicable.
"The member of staff was apparently making them stand inside the cupboard, which Nathan says has a window, on their own and then shutting the door."
Mr Sanderson added: "I would like to reassure parents that the welfare of children is our first priority and that a full and rigorous investigation is under way."
He added: "I'm sure you will understand that it would be inappropriate to comment on specifics of the investigation but please be assured that we will keep all parties appropriately informed of the findings."
Wigan Council said "swift and robust appropriate action" had already been taken.
James Winterbottom, director for children's services at Wigan Council, said: "We take allegations of this nature extremely seriously and we are pleased that members of our community have the confidence to report serious concerns like this to us.
"We have taken swift and robust appropriate action and there will now be a full and thorough investigation into the allegations. Safeguarding children is our biggest priority and parents can be assured that, following the immediate action that has now been taken, the investigation will be robust and immediate."
Any parents who have any concerns can contact Wigan Council's social care team on 01942 828300.