In a speech to the American Chamber of Commerce to the European Union later on Friday, she will say the cost of trade barriers would inevitably flow through to consumers and threaten its Europe-wide supply chain.
Ms Dawson's remarks are an attempt to shift the spotlight of the Brexit debate - which has so far focused on financial services and car making - on to the food and drink sector.
It is the largest manufacturing sector in the UK, accounting for 16% of manufacturing turnover, almost as much as the car and aerospace industries combined, she said.
Mars - maker of brands including Snickers, Maltesers, Uncle Ben's, Dolmio and Whiskas - employs more than 18,000 people across Europe, including 3,800 in the UK.
Its network of sites and factories relies on the absence of tariff, customs and other trade barriers as it moves raw materials across borders and shifts products finished in one country to be packaged, distributed and sold in others.
Ms Dawson will say: "The return of those barriers would create higher costs which would threaten that supply chain and the jobs that come with it."
Consumers would also be hit under this scenario - assuming the UK falls back onto World Trade Organisation rules.
That would mean trade tariffs of 30% in confectionery, 20% for animal products, over 15% for cereals and more than 10% for fish and fruit, Ms Dawson will say in her speech.
"Unfortunately there is no way that those costs could be absorbed without flowing through to consumers in the form of higher prices."
Mars - whose roots in the UK date back 90 years - had supported Britain remaining in the EU.
But despite the Brexit vote, Ms Dawson will say the company remains committed to the country and announced a £23m investment into its facility at King's Lynn in Norfolk shortly after the referendum.
"Our presence in Europe, including in the UK, is a proud legacy that we wish to maintain," Ms Dawson is expected to say.
The speech comes after Theresa May said Britain would be leaving the single market but would seek a new free trade agreement.
It follows a warning from CBI president Paul Drechsler that Brexit without a trade deal would expose businesses to a "Pandora's box" of damaging economic consequences.
This will be echoed in Ms Dawson's speech.
"There can be no economic advantage either side restricting trade with a large market situated on its doorstep," she is expected to warn.
"In simple terms, if the UK and the EU fail to agree on a new preferential deal, it will be to the detriment of all. Yet that realisation may not be sufficient to produce an agreement."
/Sky News/
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