Two pupils at the school have a nut allergy, which can be life-threatening for then if they come into contact with nuts.
Pupils at Menstrie found in possession of the banned tree nuts will have them confiscated by teachers.
But they'll get their conkers back at home time.
'No complaints'
Ms O'Grady told CBBC Newsround Online the school has had no complaints so far.
"Having taken medical advise I can't ignore it. If anyone wants to talk about it further they can come and ask me and I'll explain it to them.
"It's rather extreme but if you do something on medical advice you're doing it for the safety of children," said Ms O'Grady.
Kids in the school nursery can still bring nuts in to learn about as there are no nut allergy suffers in that class, she added.