The worst-damaged building, at 61 Molesworth St, was known to be earthquake-prone, he said.
"The reason I'm asking officials to look at the Stats Building is because it's a relatively new design building, and there has been a collapse of the floor in one corner."
The five-storey building on Wellington's waterfront was built in 2005.
Smith said it was on reclaimed land, which amplified the level of shaking during earthquakes. Monday's quake was also unusual because of its length. The shaking lasted for 90 seconds, compared to 12 seconds for the devastating Christchurch quake in 2011.
"That means the building has to take a lot more to-ing and fro-ing, and that may be one of the design issues that's investigated."
After the Canterbury quakes, the building code was updated to take into account the type of soil buildings were constructed on and the way it could amplify shaking during a quake. However, this took place after Statistics House was built.
The owners of the building, Centre Point and the Wellington City Council, welcomed the investigation, Smith said.
The minister also emphasised that the type of earthquake which struck on Monday was particularly strong for properties between five and 10 storeys.
Another type of earthquake could severely impact one or two-storey properties, he said.
"I am concerned about the commentary of some people, for instance on Cuba St that had one or two-storey earthquake prone buildings, who have now got the view that their building is quite safe because they did not suffer significant damage from Monday."
Council inspectors have identified 60 buildings with signs of structural damage in Wellington, though some of them were already known to be earthquake-prone.
