RNZ understands an investigation has begun after staff at the Highbrook vaccination centre in East Tamaki, Auckland, last month realised there was an extra vial left over at the end of a day of 732 vaccinations.
It indicates people may have been given saline - a salt water solution - instead.
Vaccinologist Helen Petousis-Harris, a member of the Government's Covid-19 immunisation implementation advisory group, this morning explained to RNZ the mistake would have happened during the process of readying the vaccine for use.
The Ministry of Health confirmed the vaccine stock did not match the number of doses administered, but has not yet detailed the exact date this happened.
People who went for inoculation at the Highbrook vaccination centre told RNZ they were worried, felt vulnerable and were unhappy the ministry had not proactively made efforts to contact people.
National's Covid-19 Response spokesperson Chris Bishop said it was concerning the vaccination centre had not figured out who may have missed out on the vaccine.
"It's critical that we figure out as soon as possible who these people are ... and make sure they get vaccinated because the last thing we want is people thinking they're vaccinated, walking around, when they're actually not."
He said he hoped it had not happened elsewhere, and more transparency from the ministry and the government was needed.
"Be up front with the public around whether it's happened in other parts of the country and indeed in Auckland as well."
That it had taken about a month for the information to be made public was also concerning, he said.
"We'll be asking questions today through select committee and potentially when Parliament comes back about how exactly this happened in the first place and what's being done to make sure it doesn't happen again.
"It's absolutely imperative that as we roll out the vaccine and people get the right dose and they get the record that they've had the dose, and that those records are stored securely."
"We need to figure out exactly what's happened and make sure it doesn't happen again."
ACT leader David Seymour said the Government needed to come clean and explain to New Zealanders what it knew and what it did not.
"New Zealanders know that the situation is hard, all we want is openness and transparency from our government," he said.
"If the Government doesn't have good data on ... which people were given saline solution then that's a real disappointment, but New Zealanders would be much more forgiving if they just fess up, tell us what went wrong and what they're doing about it rather than the whiff of a coverup which undermines everybody's confidence in this critical vaccine rollout."
The government needed to explain what it would do about the problem.
"Terribly disheartening for those people who may have waited some time to get vaccinated, now aren't sure whether they actually were.
"Everybody who was vaccinated at that site is now a potential candidate ... it may be that they need to revaccinate people who were vaccinated on that day.
He also said the government needed to come clean if there were other instances of this kind of mistake.
"We have to take them at their word that this is a one-off. If there are other instances that they are investigating then of course they should be transparent about that. It's critical that New Zealanders have confidence in the vaccine rollout because slow as it may have been it is still our best hope of getting our way of life back without endless lockdowns."
"People have a right to know because confidence in the vaccine rollout is critical to New Zealand success in getting on top of Covid."
National director for the Covid-19 vaccination and immunisation programme Jo Gibbs said contact would be made once the circumstances of the incident were fully understood, so people could be given appropriate advice.
The Code of Health and Disability Services Consumers' Rights gives all consumers the right of open communication with a provider.
Australians offered extra shot
A similar instance has occurred in Australia at Rockhampton Hospital in Queensland last month.
It resulted in six people receiving an ultra-low dose of the vaccine and may not have been vaccinated.
All 159 people who received the vaccine that day were contacted within a week and were offered a repeat dose.