Mr Brown said museum staff were contacting accommodation providers, schools and tour and event organisers who have bookings, museum volunteers and other stakeholders to advise them of the closure.
On the Rotorua Museum Facebook page staff said:"At this stage we will run free guided 'outside the museum tours' that take in the Government Gardens and we'll even throw in some falcon watching ... Let's make an unexpected situation great."
Rotorua Lakes Council undertook earthquake risk assessments of its buildings in 2011 after the introduction of new regulations prompted by the Christchurch earthquakes.
Several council buildings were identified as being at risk, including the older, central part of the museum which dates back to 1908.
As part of council's earthquake strengthening work programme, engineers were already scheduled to be at the museum next Monday to undertake a detailed seismic assessment.
Meanwhile, preparation for earthquake strengthening of the council's iSite on Fenton St is under way after the previous precautionary closure of the clock tower part of the building.
The historic part of the Sir Howard Morrison Performing Arts Centre had earlier been identified as being an earthquake risk and a detailed seismic assessment is under way.
Cracks in plaster on walls in the historic part of the centre after this week's earthquake were assessed as superficial.
Visual checks of other council buildings and facilities this week found no damage.
Mr Brown said new cracks have appeared down walls on the ground floor of the old section of the museum, mainly in the corners.
"We don't know if these are just cosmetic or something more.
"Overhead in the basement walkway there have been cracks for many years and a few of these appear to have widened."
Mr Brown said the museum was coming into the busy summer period. In the coming week, more than 500 people were pre-booked as part of school visits or tour group visits including 100 cruise ship passengers.
"We have contacted all pre-booked groups and they have been very understanding."
Staff had changed the venues for four out of five events scheduled over the next week or so.
Details of these events and new venues were updated on the Rotorua Museum website and Facebook pages.
Rotorua mayor Steve Chadwick said it was a wise decision to close the building.
"It needs thorough assessment to work out the extent of the damage and how much it's going to cost. Closing it was exactly the right decision and one we had to make for public safety.
"There's no panic, but it is a dearly beloved building - an absolute treasure.
"It is one of the most photographed buildings in the country and is one we have already poured millions of dollars into because we love it."
- Additional reporting by Stephanie Arthur-Worsop