The new levies, to be imposed from the day after a March 29 Brexit if MPs vote for a no-deal withdrawal, would force up prices on EU imports including cars and many food products.
Morrisons' chief executive David Potts said: "We will be playing our part to keep prices competitive.
"We are not immune from tariffs. A lot of bacon across the country is imported. However, we are Morrisons and therefore two thirds of what we sell is British.
"We are Morrisons and therefore we are British farming's single biggest supermarket customer and we are Morrisons and therefore we are also the second biggest manufacturer of British food in the world. 100 per cent of our beef, lamb and fresh poultry is British.
"Morrisons has got a long history of being a price fighter and a value for money retailer and therefore that means you have to work quite hard in order not to automatically pass price increases through to consumers."
He was speaking as the Bradford-based base firm announced a jump in annual profits despite a slowdown in retail sales as Brexit uncertainty knocked shoppers' confidence.
The UK's fourth biggest supermarket posted an 9 per cent rise in underlying pre-tax profits to £406m for the year to February 3.
Morrisons said toilet rolls and painkillers are some of items customers have started to stockpile ahead of a potential no-deal Brexit.
Mr Potts said: “We’ve seen quite a tick up in painkillers and toilet rolls this financial year. Whether that’s got any bearing on how people are feeling about the Brexit process, I don’t know.”
Morrisons has obtained Authorised Economic Operator status, which should speed up border checks in the event of hold ups.
The group said like-for-like retail sales growth slowed to 0.6 per cent in the final quarter, down from 1.3 per cent in the third quarter.
Overall like-for-like sales rose 3.8 per cent in the fourth quarter thanks to a 3.2 per cent contribution from the wholesale division, which includes tie-ups with McColl's and Amazon.
Mr Potts said the group saw a much more "challenging autumn as consumers were more cautious in more uncertain times".
But he said the group's turnaround was "well on track" and added that it responded quickly to the shift in consumer sentiment in the autumn as Brexit uncertainty took its toll.
He said 2018 ended well as a result.
The group also announced a special dividend of 4p a share, helping to boost its full-year investor payouts by 25 per cent.
Sophie Lund-Yates, equity analyst at Hargreaves Lansdown, said: “Credit where it’s due, today’s results are good going from Morrisons, the in store like-for-like sales growth may not be impressive, but it’s something not all its competitors are managing.
"However, the real jewel in Morrison’s crown is its wholesale supply deals with the likes of Amazon and McColl’s - £700m of sales came from the wholesale division this year – and that number is expected to hit £1bn soon enough."
The group expects to supply McColl's remaining 300 or so convenience stores towards the end of 2019.
It is also trialling converting 10 McColl's stores to Morrisons Daily convenience stores.
Last week, the group also brought the Safeway brand back to the high street for the first time since 2005, with two Safeway Daily stores opened in partnership with MPK Garages.