South Lakes Safari Zoo in Dalton said it would be closed from 9 January.
Barrow Borough Council raised several concerns about the zoo, including the closeness of the rhino dung to a fence, and the safety of walkways.
Zoo bosses said they felt "harassed" by the council and were unable to continue under such conditions.
On Thursday Barrow Council's licensing committee issued an order to the zoo to prove within 28 days that the aerial walkways were safe.
Zoo inspector Matthew Brash showed the council pictures of rotting timbers and said he and his colleagues had noted 20 slips and trips on them from the zoo's accident book.
But Karen Brewer, from the zoo, said there was only one accident listed in 2015 and two in 2014.
The council also said a pile of rhino dung was too close to a fence, providing a possible escape route for baboons, although the zoo said there had never been a baboon escape in 16 years of the dung being piled there.
In a statement, the zoo said: "We assure everyone that the zoo is safe and there is no evidence whatsoever to say otherwise.
"We are being subjected to an unprecedented attack and attempt to undermine our credibility and professionalism at every chance created.
"The management team cannot work under these conditions and hence the decisions made."
A Cumbria zoo is closing after councillors raised concerns about the potential for baboons to escape using a pile of rhino dung.