The company owns three ferry ports in the UK, at Holyhead, Fishguard and Cairnryan, and is the largest operator running services in the Irish Sea.
It told the BBC customs software due to launch in March could fail, and it may have to reduce sailings to and from Britain.
Ian Hampton, senior executive at Stena Line, said: “Anxiety is high. We can only do so much, we can’t plan on the basis of what we don’t know. So we are very anxious about the outcome.
“Overnight, a border appears, maybe trade will start to flow directly from the Republic of Ireland to the continent and it will miss out the UK as a land bridge.”
A government spokesman said it was engaging with ports with the aim of ensuring trade continues as smoothly as possible after Brexit.
“It is crucial to keep trade flowing when we leave the EU,” the spokesman said.
“That is why we are proposing a pragmatic and ambitious future economic relationship with the EU, and we remain committed to reaching agreement on the Withdrawal Agreement and future framework this autumn.”
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