The examination was scheduled to start from Tuesday.
She was, however, allowed to take a back paper examination on Monday.
The Rohilkhand University officials said that she could not be permitted to appear for the examination because her attendance was less than 75 per cent, which is mandatory to appear for the examination.
Head of the university's law department, Amit Singh, said that the woman has zero attendance and she did not even appear for the internal exams.
The Supreme Court on September 2 had directed the Additional Solicitor General to ensure that the woman and her younger brother get admission to a different Law college in Bareilly.
"The Supreme Court had clearly indicated that it was a special case as studies were not possible in the S. S. college run by Chinmayanand. Directions were given to the Bar Council of India for accommodating her transfer to the Bareilly College.
"If the university does not allow her to appear for her exams, it could be contempt of the SC order. The court of CJM has also granted permission to the law student to appear for her exams and instructed the jail superintendent to send the woman to Bareilly in police custody," said the law student's lawyer Kalvinder Singh.
The university Vice-Chancellor Anil Shukla said: "The woman has not even come for a single day after her admission here, and we cannot change the laws for just one student. We have not received any direction either from the high court or Supreme Court to allow her to appear for her examination despite zero attendance.
"There were directions for giving her admission which we did. Even the district court did not allow her any exemption in the attendance clause. In case any of the higher courts gives us direction then we will conduct her examination considering it to be a special case."
The law student along with her friends Sanjay, Vikram and Sachin were charged under IPC sections 385 (extortion), 506 (criminal intimidation), 201 (disappearance of evidences) and 35 (criminal act done with a criminal knowledge or intention) and section 67 of the Information Technology Act for allegedly extorting Rs 5 crore from Chinmayanand.
Chinmayanand was arrested on September 20 and booked under sections 376C (sexual intercourse by person in authority), 342 (wrongful confinement), 354D (stalking) and 506 (criminal intimidation) of the IPC on the basis of the complaint filed by the 23-year-old woman who studied law at a college run by his ashram.
( With inputs from IANS )