Boris Johnson has ruled out granting permission for a second while he is prime minister.
Johnson insisted there was no reason to go back on assurances given by SNP leaders in 2014 that the referendum then was a "once-in-a-generation" event.
He made the comments after revealed she is to request the power to hold a legally-binding independence referendum within days of the December 12 general election.
The SNP leader has already said she believes Labour leader Jeremy Corbyn will grant her a section 30 order if he is voted into Downing Street.
But Johnson was clear he did not want to see Scots given a second vote on the country's place in the UK.
Speaking on Sky News' Sophy Ridge on Sunday, the PM said: "I think having another referendum, I don't think people in this country think referendums are very wonderful for harmony.
"We had one in 2014, the British people, the people of Scotland, were told in 2014 that that was a once-in-a-generation event."
Asked if he would grant permission for an independence referendum as prime minister, Johnson stated: "No, I don't, I don't want to have one. But I don't see any reason to go back on that, on that assurance."
Johnson spoke out after the SNP leader urged Scots to use the December 12 election to "demand the right to choose a better future".
She told a packed rally in Glasgow on Saturday that Scotland was at a crossroads, arguing independence was a "better alternative" to Brexit and remaining in the UK.
"The General Election that we face now on December 12 is the most important election for Scotland in our lifetimes," Sturgeon said.
"The future of our country is on the line and there is no doubt whatsoever that Scotland stands at a crossroads moment."
However, Scottish Secretary Alister Jack said the Tories were fighting to "save Scotland from the uncertainty and the division of another unwanted independence referendum".
Writing in the Scottish Mail on Sunday, he said the Conservatives were "the only party which is strong enough to stand up to Nicola Sturgeon - and stand up for the majority of people in Scotland who are sick and tired of her independence obsession".
Jack stated: "We know that she will use any SNP success to demand a second referendum on leaving our United Kingdom.
"Every vote for us is a vote to say no, loud and clear, to that dreadful prospect.
"We are fighting this election not just to get Brexit sorted, but to save Scotland from the uncertainty and the division of another unwanted independence referendum.
"It is a fight we relish. We go into it with a message that could not be clearer and that we know people across Scotland want to hear."
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