A no-deal Brexit would increase pressure on the union, David Lidington has said.
Speaking on the BBC's Good Morning Scotland programme on Friday, the Cabinet Office minister said such an outcome would provide opportunities for those in favour of breaking up the union.
But he insisted that whilst a no-deal Brexit could lead to a rise in tensions, they could be eased if a deal is secured.
He said: "I think the union of the United Kingdom is under pressure at the moment.
"The fact that in the 2016 Europe referendum two nations of the UK voted to leave, two nations voted to remain, inevitably makes this a very difficult, delicate process.
"I think that with good will and a good deal, those tensions can be handled, but I think that the risk of no-deal is two-fold.
"I believe a no-deal outcome would do very serious harm to jobs, living standards and investment in the United Kingdom, and that is the consistent message I've been getting from businesses large and small.
"But also I think the pressures on the union would be greater because I think that damage that a no-deal exit would cause, the very divisive nature of the politics of such an outcome, would give heart and opportunities to those who, particularly in Scotland and in Northern Ireland, would like to see the United Kingdom as it currently exists brought to an end.
"Whereas I believe that the UK is a tremendously successful political and economic project that's given great benefit to everyone living in it."
Asked whether the prospect of a Boris Johnson premiership could lead to a rise in support for Scottish independence, Mr Lidington suggested the outcome of the Brexit negotiations would prove to be more significant than who succeeds Theresa May at Number 10.
Mr Lidington said he has voted for Jeremy Hunt to become the next PM, having initially backed Matt Hancock and then Rory Stewart in the earlier stages of the leadership election.
He said: "I think the strain to the union is there. It's not so much personalities elected as prime minister, but it's what is the outcome of the EU exit negotiations.
"I think that there will be, whatever that outcome, still great advantages for Scotland and every other one of the four home nations in sticking together.
"Because if you think, for example, about the United Kingdom-wide single market - the ability for businesses in Scotland to sell and to buy from businesses right across the United Kingdom, customers everywhere in the UK, without any sort of check or tariffs, that's a really important opportunity and Scottish business sells far more to the rest of the UK than it does to the EU 27."