Chris Keates, general secretary of the NASUWT union, has complained "in the strongest possible terms" to the Government and the Joint Council for Qualifications, which represents exam boards. She said the new rules were a challenge to teachers' integrity and an "unwarranted attempt to over-ride contractual provisions".
The workload agreement, between the Government, employers and unions, identified 25 jobs that schools could no longer ask teachers to perform.
Invigilating was included.
The new rules, which come into force this year, allow only teachers performing the role of administrators or invigilators to check the papers in the first hour - and they cannot leave till that hour is up.
The Department for Education and Skills is investigating. "We are aware of the new instructions and are talking with the JCQ about them," a spokesman said.
The council said the new rules were not intended to breach the workload agreement, but to protect teachers from potential accusations of malpractice. A spokesman confirmed the council was in discussions with the DfES.
The agreement allows teachers to check papers and confirm the identity of candidates at the start of exams, but schools are required to hire support staff to oversee the rest of the exams.
Schools have implemented this in different ways: West Park school in Derby paid its lunchtime supervisors to oversee exams; nearby St Benedict RC school hired parents and former pupils.
Chris Keates said the requirement that teachers remain in the exam hall for the first hour - until the last late candidates had been admitted - was offensive.
"It has the clear implication that their professional integrity is in question and that they cannot be trusted to maintain the confidentiality of the examination," she writes in her complaint.
John Dunford, general secretary of the Association of School and College Leaders, said in a letter of complaint that the new rule represented "an appalling lack of trust".
DfES guidance says exams must be overseen by support staff, not teachers:
"Invigilating examinations is not a productive use of teachers' time."