Andrew Hampton, the director-general of New Zealand's General Communications Security Bureau, said in a statement that Spark had notified it of plans to use Huawei equipment in its 5G rollout and the agency had declined it permission to do so.
GCSB is the country's main spy agency and regulates network security under the Telecommunications Interception Capability and Security Act.
Spark said in a statement that it had notified Hampton of its proposed approach to implement 5G technology, using Huawei equipment in in its planned 5G radio access network.
Spark said it had not had an opportunity to review the reasoning behind Hampton's decision and would consider any further steps after a review.
"While we are disappointed with this decision, we are confident that the decision will not affect our plans to launch Spark’s 5G network by 1 July 2020, subject to the necessary spectrum being made available by the New Zealand Government," Spark said.
Australia banned Huawei and fellow Chinese vendor ZTE from any role in its 5G networks back in August.
In recent days, there have been reports that the US is stepping up its campaign to get Huawei banned from use in countries that it counts as allies.
Contacted for comment, a Huawei spokesperson said: "Huawei is aware of Spark's statement, and we are looking into the situation. As the GCSB has noted, this is an ongoing process. We will actively address any concerns and work together to find a way forward.
"As a leading global supplier of telecoms equipment, we remain committed to developing trusted and secure solutions for our customers.
"Huawei's 5G equipment is already being deployed by major carriers around the world, with whom we have signed more than 20 commercial 5G contracts. This, alone, is a testament to our position as a leading global supplier of 5G technology.
"Moving forward, we will continue to provide our customers with innovative and secure 5G solutions."