The black-and-white film, which was revealed by The Sun, shows the Queen with the Queen Mother, her uncle Prince Edward and sister Princess Margaret raising their arms in the gesture that became synonymous with Hitler's Germany.
The Palace has threatened legal action and is looking into the source of the leak to the newspaper - but it seems it could originate from the royals themselves.
Far from being stolen, the 1933 footage could in fact have been released to documentary makers inadvertently. Part of the same movie appeared in a Royal exhibition last year, The Telegraph reveals today.
A photo from around 1933 of two-year-old Princess Margaret (seated) with her sister Princess Elizabeth, now the Queen
An edited clip, showing Princess Elizabeth and her sister Margaret talking just seconds after the 'saluting' incident featured in an exhibition at Buckingham Palace last year.
The footage was from a series of Royal home movies that were made public for the first time, though the Royal Childhood exhibition did not include the salute footage.
The Sun published pictures from the footage and The Queen is said to be "livid"
"It is believed the controversial scenes that have now emerged may have been accidentally passed on to interested documentary makers, a copy of which then found its way to the Sun," The Telegraph reports.
A spokesman for Buckingham Palace said: "There is an inquiry going on to find the source of the footage and until that inquiry is completed we would not give out any further information."
Hugo Vickers, the Royal biographer told the newspaper: “I do not believe this was stolen from the archives. What may have happened is the footage was inadvertently left in or the person releasing it did not see the sensational possibility of it.”
The release of the series of films for the exhibition is thought to have prompted many requests for access to them, especially ahead of special programmes for The Queen's 90th birthday celebrations next year, and her becoming the longest-reigning British monarch in September this year.
The grainy footage from 1933 shows the Queen, aged six or seven, playing with a dog on the lawn in the gardens of Balmoral, The Sun claims, before she raises an arm to wave to the camera with Margaret.
The Queen Mother then makes a Nazi salute and after glancing towards her mother, the Queen mimics the gesture.
The Queen Mother repeats the salute, joined by her uncle Prince Edward, the future King Edward VIII, and Margaret raises her left hand before the two children continue dancing and playing on the grass.
The film has generated particular interest because the Queen's uncle Edward, who later became King Edward VIII and abdicated to marry the American socialite Wallis Simpson, faced numerous accusations of being a Nazi sympathiser.
The couple were photographed meeting Hitler in Munich in October 1937, less than two years before the Second World War broke out.
The 'saluting' footage is thought to have been taken in around 1933 when Hitler was rising to power in Germany.
Edward VIII met with Hitler in 1937
A source told the Sunday Mirror that the Queen was apparently "livid" at the leak.
The source said that Her Majesty felt "betrayed" by "deliberate mischief making" and demanded to know how the film got into the hands of the Sun.
It is understood that depending on the outcome of the investigation, the Palace will be looking at issues of copyright and possible criminality.
A Channel 4 documentary will also probe the Royal Family's links with Nazi Germany, in a programme which will show Prince Philip aged 16 at a Nazi funeral procession for his older sister Cecile, who was killed in an air crash. It will air on July 30.
When the footage of The Queen was released, a Palace spokesman said: "It is disappointing that film, shot eight decades ago and apparently from Her Majesty's personal family archive, has been obtained and exploited in this manner.
"The Queen is around six years of age at the time and entirely innocent of attaching any meaning to these gestures.
"The Queen and her family's service and dedication to the welfare of this nation during the war, and the 63 years The Queen has spent building relations between nations and peoples speaks for itself."