The Human Rights Commission wants more options for disabled people to secure a space in MIQ.
It had received 30 complaints about the online booking portal, including claims that it discriminates against older people, disabled people and blind people who can't fill in the form quickly enough to get a voucher.
Meg Douglas Howie, who designs web services for the government, is among the complainants.
She said she was spurred to action after learning the President of the World Blind Union, from Auckland, couldn't book an MIQ spot.
"If you're someone who uses websites more slowly - and that could be for a bunch of reasons, for example you're older and you've got arthritis or you're blind and you're listening to the dates being read out on a screenreader... it means you don't get a chance to get those dates when they come up," she said.
She said the Ministry of Business, Innovation and Employment could provide more equal access through a lottery system or wait-list but, instead, it had suggested asking a friend or travel agent for help.
"That's not how accessibility works. If you're telling someone that they need to ask for help to use a website, you're actually disabling that person," she said.
In a statement, Disability Rights Commissioner Paula Tesoriero said that suggestion could "further diminish the agency and autonomy of a disabled person."
She said disabled people have an equal right to access public information, and the MBIE was a signatory to the Accessibility Charter.
That meant it had committed to meeting web accessibility standards and offering a range of accessible formats like audio, large print and easy read options, she said.
"It would be disappointing if any disabled person could not access any government service because of their disability," she said.
"I encourage MBIE to partner with disabled people to make sure appropriate design solutions are put in place."
MBIE's joint head of managed isolation and quarantine Megan Main said its goal was to make MBIE's systems as accessible as possible..
"We are aware that not everybody has the ability to use the system for various reasons including disability, no access to a computer or mobile phone, unreliable internet, constrained time, or a desire to outsource the task. For that reason the system was built with the ability for third parties to book vouchers on behalf of others."
She said in a statement that third parties could include companies such as travel agencies, or a person the traveller trusted such as a family member or friend.
Government agencies have accessibility standards they must meet for their websites and MBIE follows these.
Since the booking system was introduced, more than 200 improvements had been made to it.
Enhancements made last month included not having re-enter details each time a person refreshed the page. "That means they stay ready to book when a place comes up."
Earlier, MBIE noted a wait list would be "extremely complex" and present other challenges.
"It would not guarantee people vouchers, it would only save their place in a queue, where demand is still significantly greater than supply. We don't want people who don't need vouchers anymore because their plans have changed staying on a waitlist, which means people are waiting months for a voucher."
The Ministry is also working on ways to alert people that vouchers are coming up, it said, "while making sure we don't overwhelm the system."