During this time the diplomat was allowed to travel home.
The incident at the Stamford Hotel came on the second evening of a meeting of a multinational commission to manage the South Pacific fishery.
The commission includes members ranging as far in distance and size as Belize and the Cook Islands through to China and Russia.
New Zealand is also a member of the commission.
Mr Ponia, asked about the incident, said: "I have no comment to make."
He asked for questions to be emailed but made no further response to a written query.
The callout was news to the Cook Islands' High Commissioner, Tekaotiki Matapo.
"First time I've heard of it," he said. "That's unlike Mr Ponia."
A spokesman for the Ministry of Foreign Affairs and Trade in Wellington said it was told that, "on assessing the situation, police decided no action was necessary".
Mr McCully's office said the minister had been briefed on the police callout the following day.
A spokesman said the minister was told the "incident was minor and the police had decided no further action was required".
Mr Ponia, as head of the ministry, answers to Cook Islands Prime Minister Henry Puna, who holds the fisheries portfolio.
Ben Ponia
*Secretary of Marine Resources.
*Educated at Waikato University, earning a degree in chemistry then a masters through research on pearl culture.
*Worked for the Secratariat of the Pacific Community setting up aquaculture programmes and sourcing donor funding.
*Previously held a research role at the Ministry of Marine Resources, which he now heads.