A Brazilian couple have been kicked off a cruise ship in Dunedin after landing in hot water over the theft of a designer handbag.

Senior Constable Steve Tvrdeic, of Port Chalmers, was called to Port Otago this morning after the theft on-board the Celebrity Solstice.

He said the pair would now have to make their own way home.

The theft of the $US400 ($NZ608) Michael Kors bag happened as the ship was on its way to Port Chalmers from Fiordland with a 59-year-old woman caught on camera taking the bag after staff noticed it was missing, Snr Const Tvrdeic said.

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The cruise ship company, Celebrity Cruises, had not pressed charges, but on-board security notified police as they came in to port.

The company was helping the woman and her partner arrange flights back to Brazil.

Snr Const Tvrdeic spoke to the passengers through a Portuguese interpreter and believed they were "distraught''.

"She has ruined their holiday. It's just an unfortunate set of circumstances and people should know better.''

Snr Const Tvrdeic could only remember being called to cruise ships three or four times in the three years he had been working at Port Chalmers, as behaviour on the ships was usually good.

Last year, a woman and her partner were kicked off a cruise ship after she threatened to jump overboard when she was drunk.

According to the Celebrity Cruises website, the Celebrity Solstice is one of its "more decorated ships at sea'' and features shops, a casino, multiple restaurants and glass blowing classes.

It has an occupancy of 2850 passengers and 1500 crew.