The winner of the final will represent Oceania at next year's Confederations Cup in Russia.
The All Whites see the Confederations Cup as important preparation before their bid to qualify for the 2018 World Cup but Wood said family came first.
"I'm gutted I won't be able to take part in the final but my sister's wedding is something I've looked forward to for a very long time and it's something that is very important to me," the 24-year-old, who scored the winning goal in the semi-final against New Caledonia, said in a statement.
"My family is the most important thing in my life and to be there is a massive thing for me."
New Zealand coach Anthony Hudson said Wood had flagged the schedule conflict over a year ago.
"He came to me a long time ago but as you get nearer to a tournament you want to try to see if there are any other options," Hudson said.
"You think maybe Chris will come in and, with more discussions, you might be able to sway him the other way.
"But once I'd heard it from his mouth and seen in his face what it meant to him, it was no problem with me."
The Oceania Nations Cup doubles as the second stage of World Cup qualifying for the region. The top six teams advance to the third round next year.
The winner of the third round then plays an inter-continental tie against the fifth-placed nation in South American qualifying in Nov. 2017.
New Zealand have dominated the Oceania confederation since Australia departed for Asia in 2006.
The All Whites qualified for the 2010 World Cup in South Africa but missed the 2014 tournament in Brazil after being hammered 9-3 on aggregate by Mexico in the playoff.
(Reporting by Greg Stutchbury; Editing by Ian Ransom)
