The tabloid claimed that the "Queen Backs Brexit"
The newspaper claimed the monarch had made her comments during a lunch with the pro-European former deputy prime minister Nick Clegg during a lunch at Windsor Castle in 2011.
The front page of today's (March 8th) issue of The Sun
Mr Clegg dismissed the story as "nonsense" and accused Brexit supporters of trying to "drag the Queen for their own purposes into this European referendum debate."
Buckingham Palace insisted Queen Elizabeth II remained neutral in the debate ahead of the referendum on 23 June.
A Buckingham Palace spokesman said: "We can confirm that we have this morning written to the chairman of the Independent Press Standards Organisation to register a complaint about the front page story in today's Sun newspaper."
The palace has complained under clause 1 of the Editors' Code of Practice, which says the press should "take care not to publish inaccurate, misleading or distorted information or images, including headlines not supported by the text."
The story was published under the headline "Queen Backs Brexit". It quoted a "senior source" saying those at the lunch were "left in no doubt at all about the Queen's view on European integration.
Mr Clegg told ITV's Good Morning Britain: "It is not true. I have certainly, absolutely no recollection of a conversation like that, which I suspect I would have remembered if it had taken place."
He added: "I just think it's wrong that people who want to take us out of the European Union to now try and drag the Queen for their own purposes into this European referendum debate."
In his role as president of the Privy Council, Mr Clegg took part in a number of meetings, including one at Windsor Castle on 7 April 2011, however, it is unclear if the meeting included the lunch referred to in The Sun's article.