Louise Cook, chief investigator of accidents, said there were reportedly 38 passengers and three crew on-board the 17-metre catamaran, on a wildlife cruise.
They were evacuated to nearby boats and no injuries were reported.
Cook said getting the facts straight was vital, and she was keen to hear from people who were on-board or witnessed the accident, and to receive any photos or video footage.
The investigation team would be travelling to Akaroa "as soon as practicable", TAIC said in a statement.
Over the next several days, they would be seeking and recovering any wreckage, securing electronic records - including photos, videos, and location data on people's cellphones - and interviewing witnesses.
Following the accident, passenger Chris Friedman - visiting from San Francisco - told RNZ it was a stressful experience on his last day in New Zealand.
He said there was a loud sound, as if the boat had run over something, and he thought it might be a rock. It was followed by a whizzing sound that could have been from the engine.
"We were never really fearful that we were going to go down with the ship, but there was a teenager on-board who was quite scared and was crying, and there was also an older woman who was rather traumatised," he said.
The passengers were taken to the main wharf at Akaroa and no one was injured, he said.
Environment Canterbury said it was monitoring and assessing the catamaran to minimise the impact of any fuel leaks or debris on the environment.
"We are working alongside the owner, emergency services, the Department of Conservation, Maritime New Zealand, iwi and the local community."
Black Cat Cruises said it was the first time in more than 40 years that anything like this had happened.
It was launching its own investigation, and said it would also be working with authorities.
