A source close to Home Secretary Priti Patel has branded Ben and Jerry's ice cream "overpriced junk food" after the company criticised her stance on cross-channel migrant crossings.
In a series of tweets, the firm urged her and others to show more "humanity", adding that "people cannot be illegal".
The government earlier said the UK must consider changing asylum laws to deter migrants from crossing the Channel.
More than 4,000 people have made the journey successfully this year.
On Saturday, the Home Office asked defence chiefs to help make crossings of the dangerous route in small boats "unviable".
On Tuesday, the official Ben and Jerry's UK Twitter account posted several tweets tagging the home secretary, which began: "Hey @PritiPatel, we think the real crisis is our lack of humanity for people fleeing war, climate change and torture."
It added: "People wouldn't make dangerous journeys if they had any other choice."
The account also tweeted: "People cannot be illegal."
Rum with reason?
It's not long ago that corporate statements on anything even tangentially political were anodyne to the point of being crashingly boring. And that's if they said anything at all.
Well, things have changed. Brands, big and small, feel increasingly confident about getting stuck in on social media.
The risks are obvious: in a space that revels in the pithy, binary and divisive, to proclaim is to pick a side - and so potentially irritate a sizeable chunk of your customers.
So why do it?
To stand up for something you believe in, sure - but also to act as a brand multiplier, to get people talking about you and your stuff.
To catch the public mood, or at least a majority of it.
The curious thing with this intervention, directly targeting the home secretary, is that Priti Patel has said very little publicly about what's been happening.
But a Home Office source replied: "Priti is working day and night to bring an end to these small boat crossings, which are facilitated by international criminal gangs and are rightly of serious concern to the British people.
"If that means upsetting the social media team for a brand of overpriced junk food, then so be it."
And Foreign Office minister James Cleverly tweeted: "Can I have a large scoop of statistically inaccurate virtue signalling with my grossly overpriced ice cream, please?"
Ben and Jerry's - founded in 1978 by best friends Ben Cohen and Jerry Greenfield - was purchased by the multinational company Unilever in 2000 for around $326m (£246m).
Last week it announced it was extending a halt to paid advertising on Twitter, Facebook and Instagram until the end of this year, accusing the social media giants of doing too little to remove hateful content misinformation.
Earlier on Tuesday, Prime Minister Boris Johnson said it was currently "very, very difficult" to legally return people who arrive in the UK from France using small boats.