A statement on the OFC website confirmed the governing body's decision to uphold a protest lodged by Vanuatu after the 2-0 win to the 'Oly Whites'.
New Zealand's team included Wellington Phoenix players Louis Fenton and Alex Rufer, as well as Central Coast Mariners star Storm Roux, with the New Zealand Herald confirming South African-born Deklan Wynne is the ineligble player.
"We strongly refute the ruling regarding the ineligibility of the player in question and we will be challenging this decision," a statement from New Zealand Football chief executive Andy Martin read.
The OFC is yet to release details of the nature of the eligibility breach.
Vanuatu will contest the final of the tournament against Fiji, having been awarded a 3-0 win over New Zealand. The winner of the decider qualifies for Rio 2016.
"In accordance with Article 7 of the Regulations Governing the Application of the Statutes, a member of the New Zealand U-23 squad has been deemed ineligible to represent New Zealand," the statement read.
"In accordance with Article 13 of the FIFA Regulations for the Olympic Football Tournaments, the Committee has found that New Zealand fielded an ineligible player in the match against Vanuatu held on 10 July 2015."
It will be the first time New Zealand misses out on the Olympics football competition since Australia left the OFC in 2006.