Batsmen Craig McMillan and Lou Vincent, all-rounder Scott Styris and fast bowler Ian Butler have all cancelled plans to make the tour of Pakistan.
New Zealand Cricket (NZC) boss Martin Snedden is discussing the threat with the government and trying to ascertain whether the threat is genuine.
Snedden commented: "We have notified the International Cricket Council (ICC) and the Pakistan Cricket Board (PCB) of the threat and have entered into a consultation process with them.
"That process is expected to be completed over the next three or four days."
New Zealand's tour is scheduled to begin in Faisalabad on November 22 and is the latest in a series of cricket series in Pakistan that have been blighted by security issues.
New Zealand's last tour to Pakistan in May last year was cut short after a bomb exploded outside their Karachi hotel, killing 14 people.
Concluded Snedden: "Following the traumatic experience in Karachi when the Black Caps last toured Pakistan we agreed that individual team members could make themselves unavailable if they were seriously concerned about safety."
The decision to proceed with the tour was made by NZC only after a review by an independent security adviser.
