Police say the threat was made against the Kilbirnie Masjid on Thursday.
A police spokesperson said the teen was arrested and taken into custody on Saturday "in relation to a threat towards a place of worship in the Wellington area".
He assisted police with inquiries and was later formally charged with causing harm by posting a digital communication.
He was due to appear in the Dunedin District Court this morning, police said.
The mosque suspended all activities while the threat was investigated, The New Zealand Herald reported.
A note from the Wellington Islamic Centre said the threat was made online and "specified the exact address of the Kilbirnie Masjid".
All the other mosques and Islamic centres in the Wellington area were advised of the threat.
A spokesperson for the mosque said the decision to pause activities was made out of caution and a regard for community welfare.
"Our priority is the safety of our people and neighbours.
"We are co-operating fully with police as they investigate."
Community leaders called for calm and solidarity, reminding the public threats of this nature deeply affected the Muslim community, particularly as the mosque served as a major centre for worship and outreach in Wellington.
