She said it was the second time she had caught Radcliffe filming as she had also stumbed upon the action on Queen St yesterday.
"It was a fluke," she said.
"He waved, it was definitely exciting."
With a hot tea and fries in hand Park said she could "watch him all day".
Radcliffe, who has been spotted with his girlfriend Erin Darke around town, had previously said he was thrilled to be in New Zealand.
"I am massively excited to be here in Auckland starting filming on Guns Akimbo," he said.
"Jason Lei Howden (The Wolverine) has written a brilliant and delightfully insane script, and working with him as director and alongside the fantastic Samara Weaving to bring it to life is going to be a lot of fun.
"If you see me around Auckland looking very worse for wear and covered in blood and bruises, don't worry, this is probably for filming."
Kiwi producer Tom Hern (The Dark Horse) said: "I'm delighted to be hosting Daniel Radcliffe and Samara Weaving, as well as our German partners, for this exciting co-production between Germany and New Zealand.