Infantino, who is seeking re-election next year, has faced open revolt after three confederations - UEFA, the AFC and CONCACAF - called for a review of his leadership.
The confederations have attacked his conduct over the aborted bid to bring private investment into the World Cup and other FIFA competitions.
The OFC, soccer's smallest confederation with 11 full members, said the region had discussed the private investment plan at a meeting.
"The OFC executive committee welcomes FIFA's decision to withdraw the FFE (FIFA Forward Enterprise) proposal and its commitment to review the issues surrounding the project," the OFC said in a statement.
"OFC recognises the progress achieved over the last decade in advancing football development in Oceania under FIFA's leadership and encourages FIFA to use the review as an opportunity to identify and implement any changes that may be necessary."
But New Zealand, the only Oceania nation to qualify for this year's World Cup, said it had withdrawn support for Infantino's re-election bid at next year's FIFA Congress.
"In addition, NZF (New Zealand Football) is also seeking an independent review of the steps undertaken to develop the FIFA Forward Enterprise scheme," it said.
"After careful consideration, NZF has formed the view that decisions and actions within FIFA have contributed to a breakdown in trust and increased division within international football, and that an independent review is required to restore confidence and trust."
Infantino's withdrawn proposal came with a $20 million grant for member associations for the next funding cycle, an amount that could have been doubled if they signed the deal.
Following a crisis meeting in Morocco last week, FIFA apologised to its 211 member associations for mistakes in the handling of the proposal and said its leadership had full support for Infantino.
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