"This would lead to a level of traffic disruption that may be unacceptable to the city but that, even if acceptable, could not be negotiated and organised in the time available," he said.
The University of Canterbury also made the call to cancel its graduation parade earlier this week.
McCutcheon said they also paid careful attention to health, safety and wellbeing matters related to the ceremonies themselves.
"I am confident that we are doing everything necessary in this regard."
Graduands were advised to go directly to the Aotea Centre because nothing had changed in respect to the timings and locations of faculty functions or other associated events.
Students have responded to the decision in outrage on social media with some saying they were "furious" this once-in-a-life-time opportunity had been taken away from them.
"Everyone is legit fuming," one person said.
Another said: "That means the gunman has won ... it's a tradition."
One said: "Hold your own procession. You don't need the university's permission to walk down a street."