James Heappey, MP hopeful for Wells, Somerset made the remarks when meeting students at Millfield school and asking how they would vote in a new Scottish independence referendum.
He has since apologised, insisting he was joking.
In a statement to the Sunday Mirror Mr Heappey said: “I made a comment - intended only as a joke - but it was inappropriate and I am deeply sorry for any offence caused.
“I wrote to [the pupil] soon after the school brought her concerns to my attention and apologised unreservedly.”
It is understood that the girl was upset by the remarks made by the MP and reported it to her parents who immediately contacted education chiefs.
Heappey, 36, was elected in 2015.
A spokesman for Millfield School refused to comment.