Christine Peden defended the decision at Pear Tree Mead Academy in Harlow, saying parents were told their Year 2 children wouldn't be performing the Nativity at the start of the school year.
Other year groups are performing the play about Jesus' birth.
One parent told the Harlow Star: "The children are devastated.
"It is taking away the concept of Christmas in this school, especially when they are all so young. I feel really sorry for the children.
"They feel they are being punished for something. The other year groups are doing a Nativity, it is just Year 2 which have had theirs cancelled."
Other parents have defended the head teacher's move, saying getting good SATs results is more important than performing in the Nativity.
Christine Peden said in a statement: "Considering the notice given, I have had no parents speak to me about concerns of their child not taking part.
"We give the privilege to Year 2 to perform a graduation play in the summer term.
"This is a special occasion of them moving from the infant stage of their education to the juniors.
"The children thoroughly enjoy this occasion and makes them feel ready for their onward journey to the upper school."