According to an email sent by Clive Goodman, ex-royal editor at the News of the World, she was "upset" by it.
The journalist added that a memo was sent to palace officers, telling them to "keep their sticky fingers out".
The phone-hacking jury has also heard one of the defendants, Ian Edmondson, is no longer fit to stand trial.
Mr Justice Saunders said that it was "not appropriate to adjourn to wait for his recovery" and discharged the jury from reaching a verdict in his case.
Former NoW news editor Mr Edmondson, 44, from Raynes Park, south west London, denies conspiring to hack phones.
'Eat the lot'
In the email to former NoW editor Andy Coulson, which Mr Goodman also had sent to himself, he wrote: "Problem is that police on patrol eat the lot... memo now gone around to all palace cops telling them to keep their sticky fingers out."
The email continued: "Queen furious about police stealing bowls of nuts and nibbles left out for her in apartments in the BP/Queen's corridor. She has a very savoury tooth and staff leave out cashews, Bombay Mix, almonds etc. Prob is that police on patrol eat the lot."
She started marking the bowls to see when the levels dipped," he added.
Prosecutor Andrew Edis QC told the jury the email said the Queen was "upset" because "apparently they were helping themselves to nuts".
He said: "They were all being scoffed by police. That irritated Her Majesty apparently."
Amid laughter in court, Mr Justice Saunders told the jury that the claim that officers were stealing nuts was "an unproven allegation".
Affair question
Later, a former private secretary to Prince Charles refused to answer questions about his private life.
The jury were previously told Sir Sir Michael Peat was targeted by NoW journalists, chasing false rumours about him.
He was asked by prosecutor Mark Bryant-Heron if he was "engaged in an affair" in January 2003.
Sir Michael replied: "Could you just explain the relevance of that question?"
The jury was then asked to leave.
After a break, the judge told the jury he had decided Sir Michael did not have to answer the question "as it was not relevant".
Mr Goodman, 56, from Addlestone, Surrey, and Mr Coulson, 45, of Charing, Kent, deny two allegations that they conspired together, and with other unknown people, to commit misconduct in public office.
Mr Coulson also denies phone hacking.
It is alleged Mr Goodman Mr Coulson paid palace policemen for copies of a royal household phone directory.
