The allegations are that students who took the exam first then passed on information to those taking it later.
At Massey, Byrnes labelled the ghostwriting as "cheating services".
"I am writing to advise that the university views such allegations very seriously, with the alleged services being regarded as cheating services.
"If, after investigation as per our processes, the allegations are upheld, the students involved would be in breach of the Requirements of Student Conduct and are likely to be found guilty of student misconduct under the Student Disciplinary Regulations."
Byrnes said it was illegal for cheating services to be advertised in New Zealand.
"If the university finds evidence of cheating services being offered, it will refer the matter to the police for their investigation and possible prosecution."