The Tanbridge House School pupil was phoned at home on Friday October 11.
The man posing as the headteacher asked to meet with the pupil at school.
He did not give his name or the name of the school.
The call was terminated.
Jules White, headteacher at Tandbridge, has since sent out a letter of warning to parents, carers and schools in the Horsham district.
He wrote: “I am writing to make you aware of a potentially serious issue that arose this morning.
“Prior to the start of school a student at Tanbridge House was phoned at their home. The caller suggested that they were the student’s Headteacher – they did not, however, give either my name or the school’s name.
“Subsequently they asked to meet the student at school. The suspicious nature of the call quickly raised an alert with the student and parent and the call was terminated.”
Mr White said the police have been informed.
He continued: “It seems likely that the caller was an adult and obviously the motives are entirely inappropriate. As you would expect, the matter has been referred to the police.
“Whilst I do not wish to create undue alarm, I felt that it was important to make you aware of the situation. Please feel free to contact either the school or police in the event of any similar action.”