Leibovitz tells the Queen she thinks her shot will look better without her crown but the Queen says: "I'm not changing anything" and walks off.
A spokesman for the BBC said the Queen is smiling in most of the footage.
The documentary, which will be shown on BBC One in the autumn, follows the Queen as she prepares for her 80th birthday and state visit to the US.
Tantrums and tiaras
The Queen is also shown telling Leibovitz: "I've had enough of dressing like this, thank you very much."
The Sun newspaper's royal photographer Arthur Edwards says the tale has revealed a "welcome" new side to the Queen.
He told BBC Radio Five Live that "it was great to see the Queen can get into a strop".
"I think Annie Leibovitz went over the mark," he said.
"Every photographer just asks for one more 'can we do this, can we do that?' but the Queen wasn't having it, and when she was asked to take off her tiara she threw a tantrum.
"The Prince of Wales has given me a couple of rollickings over the time, and now I know where he gets it from."
The Queen, however, did return to sit for the celebrity photographer and the resulting portrait has been hailed as a success.
Four official portraits of the Queen were eventually released by Leibovitz.
Leibovitz is famous for her work with celebrities - memorable images include a naked John Lennon cuddling up to a clothed Yoko Ono and a naked and a heavily pregnant Demi Moore.
The programme observes the working life of the Queen and other members of the Royal Family as they go about their duties at home and abroad.
It covers events including the Queen's 80th birthday celebrations, the State Opening of Parliament, Royal tours, investitures and garden parties.
BBC One controller Peter Fincham said the BBC had had "remarkable access" to the Royal Family.
There are more than 130 official portraits of the Queen throughout her life, many of them on canvas, by a range of artists including Rolf Harris and Lucian Freud.
Güncelleme Tarihi: 12 Temmuz 2007, 12:29