The ship, one of many owned by luxury cruise company Ponant, struck another underwater object on Thursday.
"It was entering the Milford Sounds under the directions of the pilot on board when it brushed an underwater object," said Ponant's Australian PR manager Michael Corbett.
Corbett said he assumed the object was a rock.
"There is slight hull deformation but no breach of the hull, so no water is coming into the ship," he said.
TAIC's investigation of the incident "is standard procedure," according to Corbett and won't interrupt the cruise itinerary.
Ponant operates two cruises on L'Austral in New Zealand waters, prices for which begin at A$7000 (NZ$7459).
The ship holds a maximum of 260 passengers, 132 cabins and two restaurants on board.