Another student contacted a helpline and was told the issue should be resolved within half an hour, but was still locked out of her exam.
A Massey spokeswoman said a networking fault occurred between 6.55pm and 8.15pm, which impacted the learning management system (Stream) and the website.
"Any students sitting exams during the outage will not be disadvantaged," she said.
"Students will be granted extra time in their exam to compensate the time loss and they will be allowed a second attempt to complete their exam, with all their previous answers carried over."
The service should now be back up and running as usual, she said.
Massey University was among the many that moved to online learning as the Covid-19 pandemic worsened.
Classes were moved online, where possible, in late March in an attempt to reduce the spread of the virus.
Students were told pre-lockdown to prepare to study from home for an "extended period" as the university followed guidelines to limit the spread of Covid-19.
"Adhere to social distancing measures and hygiene practices at studio and lab classes that will continue to be taught face-to-face."
In-person teaching of courses, block courses and contact courses were to be halted temporarily as long as it didn't affect the quality of teaching.
At alert levels 2 and 1, campuses would reopen for all activities (but no earlier than beginning of Semester 2) but with physical distancing and other precautionary measures.