It is not known what occurred, but TVNZ reported that White was allegedly left with a broken nose and a black eye.
A Ministry of Foreign Affairs and Trade (MFAT) spokesman said it asked the US Embassy on Monday to waive White's diplomatic immunity so police could investigate.
"The United States Government has today declined to waive the diplomat's immunity," the spokesman said yesterday.
"Therefore, MFAT has asked the United States to withdraw the staff member in question from New Zealand."
A US Embassy spokeswoman said the embassy's policy was not to comment on matters which were under investigation.
"We take seriously any suggestion that our staff have fallen short of the high standard of conduct expected of US Government personnel," she said.
"Any allegations of wrongdoing are always fully investigated."
Foreign Minister Murray McCully said MFAT told him about the incident shortly after the ministry was advised of it by police on the morning of March 12.
"Whether or not to request a waiver of immunity is a decision that rests with the Secretary of Foreign Affairs," he said.
"his occurred in the afternoon of Monday March 13, in accordance with New Zealand's policy to request a waiver of immunity when Police wish to investigate allegations of serious crimes. I was kept informed of MFAT's decision, and I am satisfied with the way the ministry has conducted this process.
"Officials in Wellington and our Ambassador in Washington DC have clearly conveyed to the United States the expectation that foreign diplomats obey the law in New Zealand and are seen to face justice in New Zealand.
"The refusal to waive immunity is disappointing, and as a result MFAT has asked that the diplomat be withdrawn from New Zealand.
"I note that the United States has said all allegations are always fully investigated."
Labour foreign affairs spokesman David Parker said MFAT followed the correct process and he hoped that the US investigations would now "make the proper inquiries".
NZ First leader Winston Peters, a former Foreign Minister, said New Zealand now had to wait for the US to investigate.
"These are allegations which we expect the Americans to fully investigate and act upon, and advise us of their actions," he said.
Greens foreign affairs spokesman Kennedy Graham declined to comment.