Te Papa is unsure how many of its 600 staff will be required to self-isolate, and whether there will be enough people left on deck to reopen the museum after a deep clean.
A traveller from Sydney who visited Te Papa on Saturday afternoon has tested positive for Covid-19 on their return to Australia.
Up to 2500 people were visiting Te Papa around the same time.
The 600 people who visited the Surrealist Art exhibition between 4pm and 5.45pm need to self-isolate for 14 days and undertake testing as outlined by the Ministry of Health.
Te Papa chief executive Courtney Johnston said they made the decision to close the building at 8.30am when the ministry confirmed the case visited the museum.
She said the building will remain closed for the rest of today and tomorrow when they will reassess the situation about whether to reopen on Friday.
"We've got our scheduled deep clean to do so that we know the museum has been cleaned and is safe to reopen for visitors", Johnston told the Herald.
Johnston said the museum has about 600 staff ranging from people working on collections to casuals in the cafes.
As of 3pm today she was still working out how many staff needed to self-isolate.
All staff swiped in and out of the building, which is how the museum is determining whether they were in the building that afternoon.
Working out how many staff were needed to open the museum on Friday depended on what was scheduled to take place in the building that day including gatherings and functions, noting restrictions would be in place under alert level 2, Johnston said.
"We will only reopen if it is safe for everyone."
The Surrealist Art exhibition will be a focus of the deep clean, but Johnston was unsure whether it might have to remain closed even if the museum could open on Friday.
Te Papa is in contact with the owners of the exhibition to keep them informed of the actions being undertaken.
Johnston said the response this morning has been "remarkably smooth", although disruptive.
"We all got pretty good at this last year and we've made sure we haven't got lax in between."
Only security guards remain on site to keep the building and collections safe while Te Papa is closed to the public.
Johnston is herself a close contact as she was in the exhibition on Saturday afternoon.