May said "now is not the time" to reopen Scotland's independence debate, though she did not rule out a referendum in the future.
"The coming negotiations with the European Union will be vital for everyone in the United Kingdom", she will say.
"And I will always ensure the voices and interests of England, Scotland, Wales and Northern Ireland are represented as we negotiate to leave the EU".
But she refused repeated questions about when the right time for a new referendum might be, leaving the door open for a vote further in the future.
Sturgeon, Scottish National Party leader and first minister of Scotland's semiautonomous government, on Monday said she wants a fresh vote for Scotland, which voted overwhelmingly to stay in the European Union, before two-year divorce talks are complete.
"It is not something to which any responsible government could reasonably agree".
But Mrs. May said her message to Ms Sturgeon was clear - "now is not the time".
And although his idea that Scotland's First Minister "has created a constitutional check and balance from thin air" is a slightly comic one - giving Scotland its familiar Brigadoon status as a place which appears from nowhere on the Westminster mental map only when it threatens to leave - his strong sense of Nicola Sturgeon's referendum decision as an important move in the United Kingdom political game provides some serious food for thought.
A Scottish Parliament vote next week on the referendum must be respected. The two parties hold a combined majority in the parliament.
May's position was confirmed by Scottish Conservative leader Ruth Davidson, who said Sturgeon's timetable for a referendum - between autumn 2018 and spring 2019 - would be "rejected conclusively".
"Right now we should be working together, not pulling apart", May said in a televised interview.
"It means taking the big decisions when they're the right ones for Britain in the long-term".
Speaking to party activists, the Tory leader said: "It is now clear that using Brexit as the pretext to engineer a second independence referendum has been the SNP's sole objective ever since last June".
Brexit Secretary David Davis said Mrs May would formally invoke Article 50 by the end of March, allowing the United Kingdom to start talks on creating a "positive new partnership" with the EU.
The SNP would refuse to nominate a successor and hope the Scottish Green party, which holds the balance of power at Holyrood, would refuse to support a ruling coalition involving Labour, the Tories or the Lib Dems able to take over. And my guess is that if she had taken that course, the United Kingdom would not now be standing where it is, on the brink of a ridiculous retro revolution for which there is no plan; and to which - despite the votes of the 48 per cent - there is now no effective opposition except that stubborn Scottish voice of dissent, for which the United Kingdom as a whole may yet find itself grateful.
Britain's future trading relationship with the bloc and any exit bill which it may have to pay are both set to be highly contentious issues in the forthcoming negotiations.