The front page of The Sun showed the queen, then aged around six, raising her right hand in the air as her mother, the late Queen Mother, does the same.
The headline on the story read: "Their Royal Heilnesses" -- a reference to the "Heil Hitler" greeting used in Nazi Germany.
"It is disappointing that film shot eight decades ago and apparently from HM's (her majesty's) personal family archive has been obtained and exploited in this manner," a spokesman for Buckingham Palace said in a statement.
While a royal source insisted that the queen would not have known the significance of the gesture at such a young age, the images threaten to cause deep embarrassment for the 89-year-old monarch.
Ten years ago, it was also The Sun, a tabloid and Britain's top-selling newspaper, which published a photograph of Prince Harry wearing a swastika armband to a friend's fancy dress party. The fifth in line to the throne later apologised.
Home movie images
The images showing the alleged Nazi salute come from a 20-second, black-and-white home movie which The Sun reported was shot at the royal family's rural Balmoral estate in Scotland in 1933 or 1934 and has never been made public before.
The video shows the young future queen briefly raising her right hand in the air three times, as well as dancing around excitedly and playing with a corgi.
The group, which also included the queen's sister Princess Margaret, were apparently being encouraged by the queen's uncle, the future king Edward VIII.
The precise nature of Edward's links to the Nazis are still debated in Britain, with some historians accusing him of being sympathetic to Adolf Hitler's regime.
He met Hitler in Germany in 1937 after having abdicated as king the previous year over his desire to marry US divorcee Wallis Simpson.
The Sun defended its decision to release the images, saying they offered "a fascinating insight in the warped prejudices of Edward VIII".
"We publish them today knowing they do not reflect badly on our queen, her late sister or mother in any way," it added.
'Decades of dedication'
A royal source speaking on condition of anonymity said that the queen would have been "entirely innocent of attaching any meaning to these gestures" at such a young age.
"The queen and her family's service and dedication to the welfare of this nation during the war (World War II) and the 63 years the queen has spent building relations between nations and peoples speaks for itself," the source added.
The source also claimed that "no one at that time had any sense how it (the situation in Germany) would evolve".
The affection in which many Britons still hold the Queen Mother, who died in 2002, is based on her and husband King George VI's decision to stay in London during World War II and visit bomb sites caused by German aerial attacks known as The Blitz.
Hitler became German leader in 1933. By the end of World War II 12 years later, millions of people had been killed in concentration camps, many of them Jews.
The queen paid a state visit to Germany last month during which she went to Bergen-Belsen, her first visit to a former Nazi camp, where some 52,000 people died, including teenage Jewish diarist Anne Frank.