Jordan Ford took to the social media site after teachers told him his dyed red hair was not acceptable for school.
He copied a picture from head teacher Keziah Featherstone's profile in which she appears to have dyed hair. Jordan posted it above the caption "This is not an example to set to other students".
Bridge Learning Campus in Hartcliffe, Bristol, said Ford posted derogatory comments about the hair colour, looks and weight of Featherstone.
But the school insists Jordan made a derogatory comment in his post, which attracted up to 50 offensive remarks from fellow pupils on his Facebook page. It is believed that the incident is one of the first of its kind in the city.
Bridge Learning Campus Chief executive Mark Davies said the social media post incited abuse and that Jordan made things worse by failing to apologise afterwards.
The post was added just before Christmas and has since been taken down, along with the comments.
Jordan's mother Patricia Hedges and father John Ford said the post was made weeks after Jordan had been sent home for attending school with his hair dyed red.
Davies said it was the first time a pupil had been permanently excluded for breaking the school's social media policy.
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