New Zealand had won the first leg of the Oceania qualifying final 7-1 in Lae last Saturday and returned home to prepare for the second leg on Tuesday.
The Oceania Football Confederation (OFC) and New Zealand Football (NZF) said on Tuesday Papua New Guinea had withdrawn from the tie due to the visa issue.
NZF Chief Executive Andy Martin was happy the team had gained an Olympic berth but would have preferred the game to have been played.
"While we're obviously delighted the Football Ferns will be making the trip to Rio, were disappointed tonight's game will not be going ahead and we wont get the chance to secure our place on the field in front of our fans," he said in a statement.
The Oceania qualifiers for the Rio men's tournament were also decided in strange circumstances following an eligibility row over New Zealand's South Africa-born defender Deklan Wynne.
New Zealand were disqualified just hours before the final of last year's qualifying tournament after Vanuatu challenged Wynne's eligibility.
Vanuatu, who had lost to New Zealand in the semis, were promoted to the final, where they lost to Fiji.
NZF and the OFC were at loggerheads for months over the interpretation of world governing body FIFA's eligibility statutes. NZF decided in November they would not take the OFC to the Court of Arbitration for Sport.
FIFA cleared Wynne to play for New Zealand on Jan. 14.
(Reporting by Greg Stutchbury in Melbourne; Editing by Peter Rutherford)
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