Some are yet to implement the service, so people are being advised to call ahead to check.
Liv, from Unichem Wellington Central Pharmacy, said since it began printing passes yesterday, about 50 people had come in and used the service.
"We've had quite a few people come in, not so much that we can't keep up and we can still stay on top of our other pharmacy practices but it's been a pretty constant flow in the last few days."
Many of those people were having trouble with using technology to download their own pass or had international forms of ID that could not be used to access their My Health account online, she said.
In Auckland, Unichem Broadway Pharmacy also began offering the My Vaccine Pass service yesterday and had a busy Saturday morning issuing passes.
Further south, Life Pharmacy Papakura was yet to implement the service but said it would be offering it from the end of next week.
People need their National Health Index (NHI) number in order to get the vaccine pass, which the pharmacy can then print out or email.
People can use the My Covid Record website, or call 0800 222 478 to request a physical copy of their pass.
Ministry of Health national digital services group manager Michael Dreyer said call centres had faced "unprecedented demand", with more than 70,000 calls to the 0800 number on Thursday alone.
There are now three call centres operating with extended hours to help people wanting to set up their My Covid Record, check their NHI number, or generate their My Vaccine Pass, which can be saved digitally or posted or emailed out to them.
The Ministry of Health has issued more than 2 million passes to more than 50 per cent of fully vaccinated people in New Zealand.
My Vaccine Pass, which is an official record of a person's Covid-19 vaccination status, will help people access places within New Zealand that require proof of vaccination under the new Covid Protection Framework which will be implemented at 11.59 on December 2.