It was not known how long the building, which was built in 1973, would be closed for but Council emphasised the closure was "temporary and precautionary".
Vervoort said Council with have to go through a planning process first and consider options from engineers. It would then need to get consent for the remedial work.
The area of concern is on the top of the third floor which primarily houses heritage material, back-of-house staff and functional areas such as a kitchenette. It sits above public areas on the second floor of the building.
Vervoort said the "building is not unsafe but it could be in a seismic event".
"That's where the risk is. If the floor went [in an seismic event] it could cascade through and cause a catastrophic outcome on floors below it."
More than 40 library staff are affected by the closure. Some of them have been reassigned to suburban libraries while others will be shifted to the Municipal Building.
A pop-up library will open in about two weeks in Council's reception lounge on the ground floor of the Municipal Building.
In October Hamilton News sought details about Council's facilities maintenance plans and seismic and structural soundness for more than a dozen Council-owned buildings and assets.
However, Council's privacy advisor declined to release the information under the Local Government Official Information and Meetings Act saying "it is intended that a report be presented to Council at its public meeting in February 2017, outlining facilities maintenance and management of Council's physical assets. As this report is expected to cover the information that would be incorporated into a response to your questions the information is being withheld at this time as the information requested is, or will soon be, publicly available".
The newspaper has since laid a complaint with the Office of the Ombudsman about Council not providing the requested information and the Ombudsman has confirmed it will investigate the non-disclosure.
Vervoort said at a media briefing about the library's closure that the seismic assessment on the library had been commissioned "a few months back".
Following the Kaikoura earthquake on November 14, which was felt widely throughout the region, Hamilton News asked if Council had any of its buildings inspected by engineers for damage.
Vervoort said: "All the Council's facilities were inspected on Monday morning by the asset managers at each of the facilities. There was nothing found that would require any of these buildings to be closed. If there had been any significant damage found, we would have closed the building straight away for the safety of staff and the community."
Council closed Founders Theatre in March after it was found that the theatre's flying system posed a health and safety risk. A subsequent seismic testing report showed the building's weakest point rates just 15 per cent to earthquake specificiation as well.
The flying system, installed in 1962, holds things like production lights, drapes, scenery, and stage effects above the stage using ropes, pulleys and weights. It also holds the fire safety curtain.
A health and safety report assessed there was a likely risk of the flying system failing at some point in time. It cannot be easily fixed or replaced without requiring other major work to the 54-year-old theatre.
At the time, Council CEO Richard Briggs said while the closure was sudden it was well-known Founders Theatre needed major work. Work had been done on the flying system in 2010 and 2014 to extend its life.
Fairfax reported in February 2015 that former mayor Julie Hardaker had raised concerns with staff that crucial maintenance was required to ensure the facility remained open.
"We're here today talking about catch up because that's what this is, catch up," Hardaker said at the time.
"We're at the cliff face now and in a couple of years' time, we are falling over it."
It had been flagged back in in 2015 that the theatre's fly tower and stage structure needed urgent work to avoid closure. Hardaker said the fly tower's lack of attention meant the asset had become dilapidated.
"If they had accurate asset management plans since then, I guess we wouldn't be having this discussion because it would have been dealt with long ago."
