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Police officers were called to the building in Wellington, about 5.25am after a man was seen with an axe outside.
"The man caused some damage to glass panels but did not attempt to enter the building," a police statement said.
A member of the public told the Herald: "I'm standing here and the window is all smashed.
"It's the entrance door to Parliament - to the Beehive, from the yard."
The two side panels also show signs of an attempt to smash them in also - with two holes now showing on the bottom half of each panel.
The wider area has been cordoned off with yellow tape, and there are barriers to prevent cars driving up towards the building.
The man was taken into custody at 5.35am "without incident," police said.
The 31-year-old is expected to appear in the Wellington District Court this morning for intentional damage and possession of an offensive weapon.