The City of Greater Bendigo discovered dry rot, termites and a breakdown of exposed timber during an inspection of the archway on Friday.

Workers fenced it off immediately and erected temporary bracing.

Mayor Peter Cox said the discovery was a "major concern".

"The safety of people has to be our number one priority at this point in time," he said.

"This does demonstrate there could be other assets that need repair and we're in the process of undertaking that audit at the moment."

The discovery comes after Golden Dragon Museum treasurer Anita Jack last month told the Bendigo Advertiser the council was not assisting with the upkeep of the precinct.

"It's not really until the tiles start falling off that (council) will actually fix (the property)," she said. 

"Things tend to get fixed once they become a danger to human life, which isn't great when you have a tourist attraction."

Cr Cox told the Bendigo Advertiser at the time that Ms Jack hadn't previously communicated her concerns to the council.

He said the council had since met with Ms Jack to learn of her maintenance concerns and agreed to undertake an audit of the property.

He said the council would continue to inspect the rest of the precinct over the coming week and determine what work needed to be done to it.

He said the council considered the museum an important tourist attraction for Bendigo and took responsibility for its maintenance.

Planing and development director Prue Mansfield said the council spent about $60,000 per year on the property for maintenance services. 

She said some works were "reactive", while others were programmed maintenance.

Cr James Williams said the council thought highly of the museum and continue to support it, but it had to be "self-sustaining".

Cr Cox said the precinct would remain open and the museum was safe to visit.

He stressed that residents could enter the precinct safely through other means and encouraged people to visit it as planned.

Anita Jack was unavailable for comment.