James Heappey, who represented the Wells constituency in Somerset, said his outburst at a debate with sixth-formers last week was only meant as a “joke”.
The girl reportedly left the meeting, later telling her father, who then raised it with the school.
Heappey later admitted the quip was “inappropriate” and added he had written to the young girl.
“I made a comment – intended only as a joke – but it was inappropriate and I am deeply sorry for any offence caused,” he said in a statement on Monday.
I wrote to [the pupil] soon after the school brought her concerns to my attention and apologised unreservedly.” James Heappey
Heappey denied claims he had told the girl to “fuck off back to Scotland”.
The Scottish National Party (SNP) has since called on the Tories to suspend Heappey, adding that saying the comment was a joke “just doesn’t cut it”.
Carol Monaghan, an SNP election candidate who is also standing for re-election told The Guardian: “This type of comment reflects the unpleasant attitudes at the very heart of the Tory party – and it sadly isn’t the first time these kind of attitudes have come to light.
“For a candidate to make this kind of remark, especially to a schoolgirl, is absolutely disgraceful – and the Tories should suspend Mr Heappey as a candidate. Mr Heappey’s protests about it being a joke just don’t cut it.
“This sort of offensive and abusive language has no place in our politics.”