The incident is embarrassing for FIFA vice president David Chung, who leads the Papua New Guinea soccer federation and the Oceania confederation.
Papua New Guinea lost 7-1 in the first leg at home on Saturday.
New Zealand media reported that visa issues were blamed for the visiting team not travelling for the return match in Auckland.
FIFA did not give a reason Monday when confirming in a statement that the playoff second leg was cancelled.
New Zealand now advances to represent Oceania at the 12-team Rio de Janeiro Olympics tournament in August.
Papua New Guinea faces being fined and suspended from future FIFA competitions.
The Pacific Ocean is also due to host the Women's Under-20 World Cup for FIFA from Nov. 13-Dec. 3.
It qualifies automatically to play in that tournament as the home team.