The incident happened at 3.30pm today, Wellington's harbourmaster confirmed to RNZ.
There is a hole in the hull but it is high on the ship, and no injuries have been reported.
KiwiRail said in a statement that while docking in strong winds, the ferry made contact with the link span - a dock ramp allowing vehicles to access the vessel.
There was some damage to the link span and the ship's hull.
There were 106 passengers and 40 crew on board, KiwiRail said.
A passenger on the ship told RNZ there seemed to be a problem berthing in the afternoon.
They said passengers were given hot chips, tea and coffee and were being allowed to leave the ferry. Cars were also disembarking.
The 4.30pm sailing from Wellington has been cancelled.
It only returned to passenger service at the end of July.
Interislander's three ferries Aratere, Kaitaki and Kaiarahi were all built in the 1990s and have been hit by mechanical problems in recent years and there has been increased debate about replacing them.
In July, ship assessors found the ferries were in better shape than previously thought, and would be fine to sail for five more years.
A similar accident tore a hole in the hull of the Kaiarahi in November last year.
The coalition government has been criticised for pulling funding to the iReX project, with the maritime union warning the cancellation cost could reach $500 million.
