Scottish independence: Monarch 'above politics', Buckingham Palace says
It also follows a statement from First Minister Alex Salmond, who said the Queen "will be proud" to be the monarch of an independent Scotland.
The Palace insisted the referendum was "a matter for the people of Scotland".
A spokesman said: "The sovereign's constitutional impartiality is an established principle of our democracy and one which the Queen has demonstrated throughout her reign.
"As such the monarch is above politics and those in political office have a duty to ensure that this remains the case.
"Any suggestion that the Queen would wish to influence the outcome of the current referendum campaign is categorically wrong.
"Her Majesty is firmly of the view that this is a matter for the people of Scotland."
The BBC's royal correspondent Peter Hunt said he understands that the comments were made in response to calls for the Queen to speak out in favour of the union and not in response to Mr Salmond's remarks.
Balmoral audience SNP leader Mr Salmond said he had an audience with the Queen at Balmoral Castle two weeks ago but would not say what was discussed.
He dismissed press reports that Her Majesty was concerned about the prospect of Scottish independence.
"I want the Queen as head of state, as Queen of Scots of an independent Scotland, as her ancestors were," he said.
Mr Salmond was speaking at a photocall outside St Giles Cathedral in Edinburgh.
He said: "I think Her Majesty the Queen, who has seen so many events in the course of her long reign, will be proud to be Queen of Scots, and indeed we would be proud to have her as monarch of this land."
The first minister said he thought the statement released by Buckingham Palace regarding the Queen's neutrality was "a perfectly satisfactory and perfectly sensible" response to the press rumours about her concern.
Under the plans for independence outlined in the Scottish government's white paper, the Queen would remain head of state.
It says: "On independence Scotland will be a constitutional monarchy, continuing the Union of the Crowns that dates back to 1603, pre-dating the Union of the Parliaments by over one hundred years. On independence in 2016, Her Majesty The Queen will be head of state."
Queen's Speech In this year's Queen's Speech at the state opening of the Westminster Parliament in June, Her Majesty said her government would proceed with plans to enhance the financial powers of the Scottish Parliament and would continue to "make the case for Scotland to remain a part of the United Kingdom".
Though the speech is delivered by the Queen, the content is written by the UK government of the day.
However, there is a precedent for the Queen commenting on a major issue that has constitutional implications.
In 1977, on the occasion of her Silver Jubilee, she informed both Houses of Parliament: "I cannot forget that I was crowned Queen of the United Kingdom of Great Britain and Northern Ireland."
The comments were widely interpreted as a royal rebuff to proposals for devolution to Scotland which foundered in 1979.
An address to the Scottish Parliament in 2002 was seen as a move away from the 1977 position.
Her Majesty warmly praised the relatively new devolved settlement, noting that MSPs were helping, with their work, to "strengthen the bonds that link the nations and regions of the United Kingdom, the Commonwealth and Europe".