Police say they located a number of items at the address, including a vehicle, and are currently speaking to a 19-year-old man from the address.
The man has been charged on an unrelated matter and police are continuing to gather evidence in relation to the Al Noor incident.
Canterbury District Commander Superintendent John Price is also asking people not to share an image, first posted to a channel on the encrypted chat app Telegram, relating to the threat.
"The further sharing of this image is causing significant distress and anxiety for members of our community," he said.
"This type of imagery has no place in Aotearoa New Zealand. It is abhorrent and will not be tolerated.
"The image has been referred to the Chief Censor for consideration as to whether it should be classified as objectionable material."
If the image is classified as objectionable, anyone who knowingly possesses or shares the image commits a criminal offence and can receive a maximum of 14 years imprisonment.
"The safety of the community is our utmost priority," Superintendent Price said.
"Police continue to work alongside Al Noor mosque, Linwood mosque, and other members of our community impacted by the terrible events of 15 March 2019.
"Police have increased patrols around Al Noor and Linwood mosques and will be maintaining a visible presence in the community as we approach the anniversary of the terror attacks.
"On behalf of NZ Police, I want to thank those members of the community who alerted us to the recent threat against Al Noor mosque.
"We ask that you continue to remain vigilant, and encourage you to report anything suspicious or concerning to police immediately."