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The cover of this week's publication - the "Menstruation Issue'' - depicted a cartoon of a naked person menstruating.
A University of Otago spokeswoman confirmed on Tuesday night the magazines were taken by proctor Dave Scott after complaints were received from Dunedin Hospital and the Dunedin Public Library.
The Campus Watch team on duty on Monday night removed the rest of the magazines from stands around the university, she said.
"This was an assumption - rightly or wrongly - that this action needed to be taken, as the university was also a public place where non-students regularly pass through."
Campus Watch staff who spoke to Critic editor Joel MacManus today about the missing magazines were initially unaware fellow staff had removed them.
Mr MacManus said on Tuesday night he considered the removal to be censorship - something he believed went against everything a university should stand for.
"We stand by the content of the magazine, and believe it touched on a number of very important issues about period poverty and trans issues, as well as breaking taboos about a bodily function that half the population experience."
Earlier on Tuesday, Mr MacManus admitted it was a "challenging cover".
He said he did not know which organisation would object to the material in the magazine to the extent they wanted to stop people reading it.
"It really is a bit disheartening."
The Critic team had worked "incredibly hard" on the magazine, which came out last Sunday, he said. Some 4500 copies of the magazine had been printed.
The paper earlier put out an appeal to students on social media asking for information on the missing magazines.
Twelve years ago, an issue of Critic was banned for objectionable material.
"I don't think anything in this issue would meet those standards," Mr MacManus said.
• More details in tomorrow's ODT