Some 15 students at Our Lady's Grammar School, in Newry, are affected, the BBC understands.
It is understood the pupils sat an A-level Sociology exam.
It is believed that exam questions, set by the AQA board, were shared on social media by a student who sat the exam earlier due to a timetable clash.
It is unclear how the alleged malpractice came to light.
However, the BBC understands that the AQA subsequently investigated the allegations, and informed the pupils of the outcome of the investigation.
It is also understood that the school and the pupils were informed of the sanctions last week.
The AQA said it could not discuss cases of alleged malpractice.
But an AQA spokesperson said: "No-one taking our exams should have an unfair advantage, so we thoroughly investigate accusations of cheating and take action when there's clear evidence against specific individuals.
"Our advice to any student who receives supposedly leaked details about an exam is to report it to a teacher straight away."
The school said that it regretted the incident.
"We regret to say that there was an incident involving some of our students in relation to one of this year's A2 examinations," it told the BBC.
"The matter was dealt with by the school and the examination board in line with JCQ (Joint Council for Qualifications) guidelines and the students involved have been sanctioned.
"There has been no suggestion of any breach of examination or invigilation protocol by the school.
"We in Our Lady's prize our deserved reputation for integrity.
"We also know the importance of care and compassion in times of difficulty and will offer support as needed to the young women involved, all of whose school careers up to this point were without blemish."
A number of pupils at a County Down school have had their grades cancelled after being disqualified from an A-level exam.