A spokesman for the Attorney General confirmed that the front of the magazine's November edition, published as Mrs Brooks's trial started at the Old Bailey, would not lead to contempt of court proceedings.
He said: "The front cover of the current edition of Private Eye has been brought to the attention of the Attorney General, but it has been decided that proceedings for a potential contempt of court are not required in this case."
Former News International chief executive Brooks is facing trial along with seven other defendants including ex-Number 10 spin doctor Andy Coulson.
Mr Justice Saunders told the nine women and three men of the jury: "Unfortunately Private Eye has seen fit today to put out their November edition. You will undoubtedly see it on the newstands, so I can show it to you.
"It bears a picture of Rebekah Brooks on the cover. It's meant to be satire. You ignore it. It has no serious input and it is not relevant to your considerations. It is one of those things that you will have to ignore - a joke which in the circumstances of today is a joke in especially bad taste."
The cover featured a photograph of Brooks under the headline Halloween Special, with Horror Witch Costume Withdrawn from Shops under the picture.
Mrs Brooks, 45, of Oxfordshire, and Mr Coulson, 45, from Kent, are both accused of conspiracy to intercept communications. They are accused of conspiring with former News of the World staff and others to illegally access voicemails.
Mrs Brooks also faces charges of conspiring to commit misconduct in public office and conspiracy to pervert the course of justice. Mr Coulson is also facing two allegations he conspired with the tabloid's ex-royal editor.