A "Mr Whippy"-style vaccine bus service is being rolled out this week and Jacinda Ardern has asked the public to come up with a name, as long as it isn't "Bussy McBus Face".

On Tuesday at a Press Conference, Ardern announced the vaccine bus service will start running from Thursday.

From Thursday six buses will visit a number of Auckland communities that have low vaccination rates or have access issues to current centres.

"The initial plan is to take them into areas where we know vaccination numbers have been low, or people have not been able to access those vaccination services as easily," Ardern said.

Across the Tasman, a similar vaccine rollout has seen the buses been called "Jabba The Bus".

But Ardern assured New Zealand's they can do better, asking the public to suggest name ideas.

"I'll leave it in the hands of creative New Zealanders. I know when you've seen challenges like this put out, you see enormous amounts of creativity."

"But I think 'Bussy McBusface' is probably already a given. Let's rule out 'Bussy McBusface' right from the beginning," she said.

The buses will expand the fleet from six to 12 in the coming weeks, Ardern said.

Many social media users found the humour in Tuesday's press conference and some even started to think of names.

"Jabba Waka" one Twitter user suggested.

"Can we just get a free ice cream with a flake, dipped in chocolate and sprinkles after we have had our jab. Now that would make me want to go even more lol," one person wrote.

"As long as it doesn't play the Mr Whippy music," another joked.