Video report by ITV News Political Correspondent Angus Walker
She warned it was now “almost inevitable” the UK will leave the European Union without a deal, despite Mr Johnson insisting an agreement can be reached with Brussels.
Mr Johnson, who was booed by protesters as he entered the Scottish First Minister’s official residence in Edinburgh, said there was a “very good chance we can get a deal”.
The PM accepted there was “no change” in the position of EU leaders – who have been consistent that they will not renegotiate the Withdrawal Agreement reached by Theresa May.
Despite that he insisted: “There is ample scope to do a new deal, to do a new deal and a better deal.”
Video report by ITV News Correspondent Geraint Vincent
But Ms Sturgeon said: “After my discussions with Boris Johnson, behind all of the bluff and bluster, this is a government that is dangerous.
“I think the path that it is pursuing is a dangerous one for Scotland and for all of the UK.
“He says publicly – and he said it to me again today – that he wants a deal with the EU, but there is no clarity whatsoever about how he thinks he can get from the position now where he’s taking a very hard line – the withdrawal agreement is dead, the backstop is dead.
“If I listen to all of that and listen to what’s not being said as well as what is being said, I think that this is a government that is pursuing a no-deal strategy, however much they may deny that in public.”
The SNP leader added: “I think, if he were in this room right now, he would deny this vehemently, but I think he wants a no-deal Brexit.”
She spoke out as Mr Johnson made his first visit to Scotland since becoming Prime Minister, starting with a tour round the HMS Victorious nuclear submarine on the Faslane naval base on the Clyde.
He then went on to have meetings in Edinburgh with Scottish Tory leader Ruth Davidson – who has made plain her opposition to a no-deal Brexit – as well as the First Minister.
After his meeting with Ms Sturgeon, Mr Johnson left Bute House by the back door.
The new PM used his visit to insist there is “no reason” for Scots to have the second independence referendum that Nicola Sturgeon is pushing for.
He hit out at the “campaign to destroy the union” from the SNP – and while he refused to unequivocally rule out granting Holyrood permission for a second independence referendum, he said comments that the 2014 ballot was a “once in a generation” event must be respected.
He stated: “It was a once-in-a-generation consultation of the people, we did it in 2014 and the people were assured then that it was a once-in-a-generation consultation.
“I see no reason now for the politicians to go back on that promise.”
Ms Sturgeon, however, made clear her desire for Scots “to chart their own course and choose their own future”.
She told BBC News: “I made abundantly clear to Boris Johnson my opposition to Brexit and a no-deal Brexit, and also made it clear to him the people of Scotland should be able to chart their own course and choose their own future, not have that future imposed upon them.”
And she claimed the new PM had “set the UK on an almost inevitable path to a no-deal Brexit”.
She added: “The position it has taken makes it very difficult to see how any deal can be struck with the EU and I think that would be catastrophic for Scotland and the whole of the UK.”
A Number 10 spokesman said Mr Johnson had told the First Minister “he was a passionate believer in the power of the Union and he would work tirelessly to strengthen the United Kingdom and improve the lives of people right across Scotland”.
The spokesman added: “On Brexit, the Prime Minister said that while the Government’s preference is to negotiate a new deal which abolishes the anti-democratic backstop, the UK will be leaving the EU on October 31 come what may.”
Mr Johnson said while he was “aiming for a new deal” with Brussels, it was Government policy to prepare for a no-deal outcome.
“That is what we are going to do with high hearts and growing confidence, we will prepare for a no-deal Brexit.”