Dame Elish sought court protection against Robert Green, a self-styled "investigator" jailed earlier this year for naming prominent Scots as child rapists.
She is using laws she championed for the victims of harassment and aims to bar Green from approaching or contacting her in any way.
Her action is the latest result of a series of unsubstantiated child sex abuse allegations made by Hollie Greig, a young Aberdeen women with Down's Syndrome, more than a decade ago.
Dame Elish is understood to hope a non-harassment order would prevent Green, who acts as Ms Greig's "lay legal adviser", using the internet to claim she covered up for a paedophile ring said to include a sheriff, a senior police officer and other prominent Aberdonians.
The former Lord Advocate's solicitor, Peter Watson of Levy & McRae, last night said: "We are seeking an order to prevent Mr Green doing anything which would amount to harassment."
Dame Elish, the prinicipal of St Hughes College, Oxford, is taking the action amid heightened concern about the behaviour of "online trolls" and cyberbullies – those who use the internet to defame or intimidate others.
Her name has been widely linked on the internet to Green and Ms Greig's claims, despite two police investigations failing to find evidence of wrongdoing.
Dame Elish and others are said to be deeply hurt by an online campaign, partly linked to Green, that have made the Hollie Greig conspiracy theory an international internet sensation.
Campaigners who call themselves "Hollie's Army" have bombarded the Crown Office, the Scottish Government and MSPs with calls and emails complaining about Dame Elish.
Some websites have previously named those Green and others believe were victims of the supposed Aberdeen paedophile ring – as well as those they believe were abusers.
Websites have also claimed that Ms Greig's uncle – who died in a car crash in 1997 – was murdered after he witnessed her abuse and that her mother was "forcibly" sectioned days after the first allegations were made.
Green was released last month after serving three months of a year-long sentence.
The former travel agent, who is 65 and from Warrington in Cheshire, was jailed after what he believes to be the most expensive breach of the peace trial in Scottish legal history.
He was convicted of breaching the peace by naming members of the supposed paedophile ring and of breaching bail conditions barring him from travelling to the north-east of Scotland.
Last night Green, who is electronically tagged under the terms of his early release, said he would contest the non-harassment order.
He said: "If I don't get legal aid I will represent myself if Dame Elish is prepared to do so too. I would love to go up against her in court even though she is much more qualified than I am."
Green denies claims by Dame Elish's lawyers that he has taken pictures of the former Lord Advocate's home.
He also says he does not know who runs a website called "Free Robert Green" which repeats some of the unsubstantiated allegations against Dame Elish.
Green is barred from approaching witnesses from his trial by a series of non-harassment orders granted by the sheriff overseeing the case.
However, Dame Elish did not give evidence and has now turned to the civil courts to obtain protection. Green faces criminal sanctions if he breaches any non-harassment order granted by the courts.
The "investigator", who always stresses Ms Greig received criminal injury compensation as a probable victim of sexual abuse, committed his breach of the peace while campaigning in the 2010 Westminster elections.
He is thought to be the only candidate to ever run in a constituency – Aberdeen South – which he was legally barred from entering. Green stood for a party called Scotland Against Crooked Lawyers.
The "Hollie" case split the party, which subsequently disbanded.