The order - until further notice - bans the agoraphobic from contacting a string of well-known people.
The list includes Mrs Mensch, her businessman husband Peter, and Mrs Mensch's ex-husband, property developer Anthony LoCicero.
Lord Sugar, the Amstrad businessman and star of hit TV Show The Apprentice, was named on the restraining order, as was Terence Blacker, a columnist with the Independent newspaper and Zimmerman's former neighbour in London.
Also listed was General Sir Mike Jackson - once head of the British Army - and David Petraeus, former US Army commander in Iraq and Afghanistan and now director of the CIA.
Zimmerman had targeted the MP for Corby, Northamptonshire, last year telling her to stop using the social networking site Twitter or face the consequences.
The agoraphobic, who lives in a run-down house in Barnwood, Gloucester, told Mrs Mensch that she faced a "Sophie's Choice" - a reference to a novel in which heroine Sophie has to choose between the life of her son or daughter at a Nazi concentration camp.
The email, which was dated August 22, 2011, said: "Subject: You have been HACKED 😀
"Louise Mensch, nee Bagshawe, the slut of Twitter.
"We are Anonymous and we don't like rude c**** like you and your nouveau riche husband Peter Mensch. You have been hacked!
"We are inside your computer and all your phones, everywhere ... and inside your homes.
"So get off Twitter.
"We see you are still on Twitter. We have sent a camera crew to photograph you and your kids and will post it all over the net, including Twitter. C***face.
"You now have a Sophie's Choice. Which kid is to go? One will, count on it c***.
"Have a nice day
"From all of us at MIT 617-253-1000."
The Northamptonshire MP, 40, who has a Twitter following of 50,000, immediately called in the police and arranged security for her family.
She went on to tweet to followers: "Had some morons threaten my children by email. To those who sent it; get stuffed losers."
The offensive email was later traced to the IP address of Zimmerman's home computer.
He was charged with an offence of sending by public communication network an offensive, indecent, obscene, menacing message or matter.
The case against Zimmerman, of Barnwood, Gloucester, had been proven in his absence after he failed to attend court - blaming his agoraphobia and depression.
He was supposed to have been sentenced at Cheltenham Magistrates' Court last week but failed to attend.
Police arrested him this morning for breach of bail, an offence he admitted once he was brought to court.
Zimmerman, who is extremely well spoken, wore a dark blue coat and glasses for today's short hearing.
The last time he had faced District Judge Martin Brown he had appeared via video link from a side room but today he was in the dock of court room one surrounded by two guards, having been brought up in handcuffs from the cells.
Passing sentence, the district judge told Zimmerman that he had committed a very serious crime.
"I have heard about the allegations and in my view they went beyond mere mischief," he said.
"These were ugly, unpleasant and serious remarks to the complainant by email. Quite understandably they caused her great concern.
"They cross the custody threshold because of the seriousness.
"Because of your age and because of your conditions and I accept that you have certain problems, although I do not accept they are as severe as you make out, I am prepared to suspend the sentence."