Frank Zimmerman, 60, who refused to attend court, emailed Mrs Mensch, who has three children, in August last year. He told her to choose which child was to die - referring to the film Sophie's Choice in which a mother has to choose between the life of her son or daughter.
Mrs Mensch had given him her personal email address after he contacted her on Twitter claiming he had information on the telephone hacking scandal.
Zimmerman also told Mrs Mensch, who writes novels under her maiden name Louise Bagshawe, that there were cameras watching her family's every move.
His email continued: "You now have a Sophie's choice. Which kid is to go? Who will you choose?" The email was traced to Zimmerman's computer.
Yesterday he was found guilty in his absence at Gloucester magistrates' court of improper use of the public communications network. He will be sentenced next month.
In a statement read to the court, Mrs Mensch described her fear at opening the email while she was in New York.
She said: "I opened the email up and it was abusive and threatening. It referred to my children and said one would die. I was more than 3,000 miles away from my children and I had no idea how to protect them.
"I felt powerless. I became extremely scared and called the House of Commons. The police made immediate arrangements to ensure my family's safety."
The court was told police managed to trace the malicious email back to Zimmerman's computer by tracking the IP address.
District Judge Martin Brown found Zimmerman guilty in his absence - but said he would only sentence him in person.
Zimmerman - who a psychiatrist previously ruled would become a "wreck" if he was forced to attend court - will be sentenced at Gloucester Magistrates Court in May.
