The Defence Force's headquarters in Aitken St, built in 2007, and Statistics New Zealand's purpose-designed building on the waterfront, built in 2005, both suffered significant structural damage.
Statistics House was hit particularly badly, having suffered a potentially fatal floor collapse.
Auckland University structural engineering Professor Jason Ingham said the floor collapse never should have happened.
"That is not what the public should expect and that is not what this profession would expect," he told the Herald.
"If it had been a daytime event on Monday morning, instead of Sunday night, then it would have been quite plausible to expect that people would have been killed."
Ingham said the worst-hit buildings in Wellington were on reclaimed waterfront land.
"There's a small pocket of buildings that have taken a very large amount of damage, so the suggestion is there was some very extreme excitation at that location."
Despite that, Ingham said he wouldn't expect modern buildings to exhibit such significant damage.
"After Christchurch, the general conclusion was that most modern buildings, designed appropriately, had performed well. We would have thought that those conclusions could be applied here also."
Engineers would now study accelerometer data to see what stresses the buildings were put under.
However, there were no accelerometer devices in the waterfront area around Statistics House.
Ingham said that was surprising, given the nearby BNZ building had suffered significant interior damage in the 2013 Wellington quakes. "We would hope that maybe there'd be more."
Canterbury University structural engineering Professor Stefano Pampanin said buildings were designed to suffer some damage to non-structural elements, such as the facade and the windows.
But damage to a structural element like a floor was generally not expected. "Typically speaking that would not be the expected response or damage under such an earthquake."
Prime Minister John Key said officials did not yet know how many Government departments would need to been relocated due to quake damage. A full review of Government buildings was under way.
"One of the interesting things is of course that Defence House is a very new building, so some questions obviously need to be asked."
The Defence Force said the full extent of the damage will not be known for several days.
"Consequently we are considering a range of options for interim solutions, including remote working and relocation of staff to other NZDF facilities."
Government Property Group director David White said all buildings occupied by government agencies were being assessed by engineers to ensure they were structurally sound.
"This has been a very significant event and buildings have stood up very well. Some have sustained some damage, non-structural, but nevertheless require clean up. In this, peoples' safety is the paramount priority.
"There are more than 100 properties occupied by government agencies in Wellington. Of these, two are currently known to have structural issues that mean people cannot return to these buildings for some time.
"A small number of other buildings have still not finalised their assessments. A number of buildings have been cleared but are still cleaning up."
Wellington Mayor Justin Lester yesterday said the city's most badly damaged building, the tower at 61 Molesworth St, would need to be deconstructed.
A plan was being worked on but Lester said it did not necessarily have to be disruptive.
An exclusion zone in place around the building was yesterday widened to include Pipitea House, built in 2011, because of concerns with its facade in high winds. The building houses the Government Communications Security Bureau and the Security Intelligence Service.
The Tennyson Apartments building on Tennyson St in Te Aro, which houses about 60 people in 23 apartments, was also evacuated because of a "severe crack".
