The British weekly newspaper said it had obtained the full 27-minute al-Qaida tape that claimed responsibility for the London 7 July bombings that killed 56 people, the four bombers included.
The Sunday Times said MI5, Britain's internal security service, had passed the warning to Elizabeth's protection team.
Parts of the video were broadcast in September on Aljazeera.
A man identified as Mohammad Sidique Khan, speaking in a northern English accent, told viewers that Western atrocities against Muslims drove him to bomb a London Underground train.
Khan, an education assistant and father of one from Dewsbury, near Leeds in northern England, was the suspected ringleader of the 7 July gang.
The video was accompanied by a separate message from al-Zawahiri, though the two were not seen together or at the same location in the tape.
Khan said Western atrocities
drove him to bomb a London train
A senior government department official told The Sunday Times: "MI5 is aware that there are some pieces of the video that have not been aired. They are aware of the bit of al-Zawahiri talking about the queen and they have notified the relevant authorities."
The full video is circulating on secure websites used to inflame and recruit terrorists, the newspaper said.
Al-Zawahiri also warns Muslim leaders in Britain who "work for the pleasure of Elizabeth, the head of the Church of England".
He said those who followed her were saying: "We are British citizens, subject to Britain's crusader laws, and we are proud of our submission."
In a possible mocking remark at the Muslim Council of Britain (MCB), a British Muslim umbrella group, which had instructed mosques to inform on potential terrorists, al-Zawahiri attacked "those who issue fatwas, according to the school of thought of the head of the Church of England".
In the previously unseen footage, Khan, 30, said: "It is very clear, brothers and sisters, that the path of jihad and the desire for martyrdom is embedded in the holy prophet and his beloved companions.
"By preparing ourselves for this kind of work, we are guaranteeing ourselves for paradise and gaining the pleasure of Allah.
Sacranie (C) said Khan's message
was trying to incite murder
"And by turning our back on this work, we are guaranteeing ourselves humiliation and the anger of Allah. Jihad is an obligation on every single one of us, men and women."
MCB Secretary-General Sir Iqbal Sacranie said the message was a "perverse interpretation of Islam".
"The victims of Sidique Khan were innocent people. It's clearly inciteful. It's trying to incite people to commit murder," he told The Sunday Times.