Val Hughes, of Sandhurst Junior School in Lewisham, south-east London, said teachers had mistakenly taken the advice of a professional photographer.
She said it was an "error of judgement" and would be personally writing to all parents to apologise.
A governors meeting will be held into the circumstances of the incident.
'Promoting diversity'
Ms Hughes said: "On this occasion, teaching staff took the professional advice of the photographer. We can see this was an error of judgement and we regret this greatly.
"Contrary to reports, however, the children were not upset in any way and really enjoyed having their photos taken.
"Our school has an excellent record of promoting diversity and I will personally be writing to apologise to all parents."
She said the school would raise its concerns with the photographer to ensure it "never happens again".
'No complaints'
Chair of governors at the school, Abdeslam Amrani, told BBC London 94.9: "Unfortunately for some reason a decision was made, not a good one though, to take a picture of children in a particular alignment.
"We [school governors] have taken this pretty seriously and we apologise to the children and the parents who were distressed by the experience."
"It was a misjudgement and we will be holding an emergency governors meeting to see how this issue has arisen and to look at making sure it does not happen again.
He said he was not aware of any complaints made by parents.
The school has just received an "outstanding" report from Ofsted and many of its pupils are achieving high grades.
A governors' meeting will be held on Monday.
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