Landcare Research's fungi expert Jerry Cooper then identified the fungus as a sandy stiltball (Battarrea phalloides), never before recorded in New Zealand.
Shepherd said they could only guess how it got there.
"Fungi have very light wind-blown spores so it's probably just blown across from Australia, similar to something like myrtle rust, which also just arrived recently."
But Shepherd did not envisage it posing a threat to our ecosystem.
"It's actually a species that's found in many countries around the world - I think 64 countries - but in most of them it's really rare so there might be only one or two plants in a population.
"Nowhere is it really common, so we suspect it's not going to be a problem here."
Shepherd said she was keen to discover whether more sandy stiltballs exist in other parts of Wellington, or around the country.
"This fungus dies down during parts of the year and then it might pop up somewhere else. So it's already disappeared from where it was, there were a couple of specimens - one I collected and the other died.
"But I'll be looking next autumn to see if any more of them pop up in the same place, or maybe even other parts of Wellington.
"I'd be really keen to hear if other people see them, I'm interested to see if it's going to spread."
The fungi finding has just been published in the New Zealand Journal of Botany.
