It is believed the teacher has been singled out due to her political beliefs and has been unable to return to the school since the threats emerged.
Councillor John Blair said: “It is completely unacceptable that a teacher going about her daily duties has been targeted in this way. No-one should be subjected to this type of treatment.
“A person’s political views should never be used to form the basis of threats or discrimination and the whole community must join in supporting the teacher, the school and her pupils as they deal with the fall-out of this callous act.
“I would call on all political parties to unite in strongly condemning these threats, made against a professional responsible for shaping the lives of young people.
“Not only is the teacher’s health and safety at risk, but this incident could also cause disruption to the education of her pupils as exam season is fast approaching. My thoughts are with the teacher in question and the most important thing now is that she recovers and feels able to return to her position at the Boy’s Model.”