President Paul Ludlow said the cruise line has withdrawn its Oceana ship, which flies the British flag, from the gulf.
The company said it had been monitoring tensions in the area and has now taken the “Difficult deciison” to call of all trips in the region untul 2020.
Tensions escalated last month as a British flagged tanker was seized by Iranian forces, with crew members still being held.
The issues date back to when UK forces helped seize an Iranian tanker off the coast of Gibraltar.
Earlier this week the UK joined a US-led mission to protect civilian ships in the Gulf.
Currently there are no ship owners who have decided to swap their British flags for that of a neutral country.
The company’s president, Ludlow, said he was concerned by its British links, which could make the ship a target for Iran.
“Whilst we appreciate our guests will be disappointed, the safety of our guests and crew is absolutely paramount,” he said.
“And given our UK status, coupled with uncertainty in the region, we have had to make this difficult decision.”
Guests will be given a full refund the company.