The person lives alone in the Vincent Residences, an apartment block in the CBD which is next to the Grand Millenium Hotel.
The hotel, which is a managed isolation facility, had a fire alarm evacuation on Monday night, but that evacuation is not likely to be the source of the infection because the woman became symptomatic that same day.
A Managed Isolation and Quarantine spokesperson earlier said guests were evacuated using strict infection control protocols including PPE, masks and physical distancing.
Anyone who visited the Vincent Residences as a visitor or a resident, since Saturday, is urged to get a Covid test and isolate until the results are returned.
Health officials will be giving another update on the case later today at 5pm.
Te Pūnaha Matatini director Professor Shaun Hendy said the Auckland case was similar to the August cluster where the source was unknown.
"Anyone in Auckland, particularly anyone who has been in the Auckland CBD in the last two weeks, should seek a test if they have any of the symptoms associated with Covid-19. Anyone who has visited A-Z Collections this week should self-isolate and seek a test," Hendy said.
He said contact tracing and/or genomics could help identify a link, but if that could not be established Auckland could be looking at moving up alert levels.
"Our testing rates and use of the app are higher than they were in early August, so I think we are likely in a better position now than we were then."
University of Auckland professor Siouxsie Wiles said the pandemic was "growing exponentially overseas, so we will likely see more and more people arriving in New Zealand incubating the virus".
"Quickly identifying any community cases means we should be able to stop any outbreaks using testing, contact tracing, and isolation rather than having to move up the alert levels."