Assistant registrar Ngaatendwe Takawira caused embarrassment for university administrators by procuring a cap which was too small for the 92-year-old leader, according to her suspension letter, quoted in local media.
Ms Takawira denies the allegations.
The president’s office is not thought to have made a complaint.
The decision to suspend Ms Takawira was probably taken by university authorities keen to appease the president and not from any genuine anger on his part, says the BBC’s Brian Hungwe in the capital Harare.
Driver ‘turned away’
Academics first noticed that the so-called “cap of knowledge” was not sitting properly on the president’s head while he was presiding over a graduation ceremony in 2014, our correspondent says.
The university then arranged for new caps to be designed for Mr Mugabe in time for this year’s ceremony, our reporter adds.
But a driver sent with the new selection of caps for Mr Mugabe to try was turned away by security guards at the president’s office, a government source, who did not wish to be named, told the BBC.
As a result, the president did not manage to have a fitting before this year’s graduation ceremony on 2 October.
Ms Takawira is now challenging the university’s disciplinary action in the country’s labour court.