Scottish First Minister Nicola Sturgeon on Monday called for a vote
before Britain leaves the European Union.
But May rejected the timescale on Wednesday, saying the UK should be "working together, not pulling apart."
Sturgeon had accused May of failing to to engage with her call for Scotland to remain in the European single market after Brexit, and that Scotland risked being taken out of the EU against its will.
But May hit back Wednesday, warning Sturgeon, leader of the Scottish National Party (SNP), should stop talking about independence and instead focus getting a good deal out of Brexit.
"When the SNP government say that it's the time to start talking about a second independence referendum I say that just at this point all our energies should be focused on our negotiations with the European Union about our future relationship," she said in a televised statement.
"And to be talking about an independence referendum will, I think, make it more difficult for us to be able to get the right deal for Scotland, and the right deal for the UK."
Scottish Secretary David Mundell said the UK government would not entertain negotiations with Sturgeon over the possibility of second referendum.
He said the referendum proposal by the SNP was "not fair" and would not allow be people to "make an informed choice."
Article 50 trigger
May is expected to trigger Article 50 later this month
, allowing for the start of formal negotiations to begin between Britain and the other 27 member states of the European Union over the country's divorce from Brussels.
The Prime Minister said it would be unfair on the Scottish people to hold a referendum without knowing the terms of Brexit deal with an agreement expected to be reached by 2019.
"More than that I think it wouldn't be fair to the people of Scotland because they'd be asked to make a crucial decision without the necessary information without knowing what the future partnership will be or what the alternative for an independent Scotland would look like," she added.
"So I think just now we should be putting all our energies into ensuring that we get that right deal for the UK and the right deal for Scotland in our negotiations with the European Union, that's my job as Prime Minister."
Before Scotland holds a referendum, the UK government must agree to the vote.
Scotland backed to remain in the EU by 62% to 38% and Sturgeon believes the shift of landscape following the Brexit vote may persuade some Scots that independence is the solution.
A spokesman for the First Minister described Mrs May's statement as "spectacularly unclear," according to the UK Press Association.
He said: "If we do get clarity that what the PM means is that discussion about a referendum should not even begin until some point after Brexit, then effectively what the PM is doing is unilaterally blocking a referendum. That would be a democratic outrage."
When questioned how bad a move it would be from May to reject Scotland's wishes for a referendum, he added: "I think it would play disastrously. I think it would be a miscalculation and a blunder of epic and historic proportions".