In a letter to Scotland’s first minister, the PM said: “I cannot agree to any request for a transfer of power that would lead to further independence referendums.”
Ms Sturgeon immediately hit back at Mr Johnson, saying that the “Tories are terrified of Scotland’s right to choose”.
Ms Sturgeon has argued Brexit, which she says takes Scotland out of the EU against its will, gives the country grounds for another vote on independence.
But Mr Johnson said in a letter to Ms Sturgeon on Tuesday: “Another independence referendum would continue the political stagnation that Scotland has seen for the last decade, with Scottish schools, hospitals and jobs again left behind because of a campaign to separate the UK.
“It is time that we all worked to bring the whole of the United Kingdom together and unleash the potential of this great country.”
He also pointed to the 2014 referendum, in which Scotland voted by 55% to not be an independent country, saying Ms Sturgeon “made a personal promise” it would be “once-in-a-generation” vote.
Ms Sturgeon responded on Twitter: “Tories are terrified of Scotland’s right to choose - because they know that when given the choice we’ll choose independence. Tories have no positive case for the union - so all they can do is attempt to deny democracy. It will not stand.
“The problem for the Tories is the longer they try to block democracy, the more they show the Westminster union is not one of equals and fuel support for independence. This response predictable - but also unsustainable and self defeating. Scotland will have the right to choose.”
In an official statement issued later, Ms Sturgeon added “the Westminster union cannot be sustained without consent” and that “democracy will prevail”.
In the House of Commons, Mr Johnson has regularly blocked SNP MPs’ calls for a second referendum.
He was even called out by the party’s Westminster leader Ian Blackford last month when he was caught “playing” on his phone rather than listening to Mr Blackford’s call for independence.
Mr Johnson, putting his phone back in his pocket, muttered back: “Say something more interesting.”