The decision comes as the women at the heart of the initial complaints say they are “deeply disappointed" and “deeply disturbed” by both the committee and the inquiry’s decision to request and provide access to the messages, which they described as “personal communications between friends who supported each other during a traumatic time”.
The messages – from the so-called ‘Vietnam’ group – were pitched by supporters of the former first minister as being key to providing evidence for a conspiracy by the SNP’s high command against Mr Salmond.
Committee members had decided to invoke never-before-used powers demanding the Crown Office hand the material over.
However, in a statement released on Tuesday, committee convener Linda Fabiani said the publication of the messages handed to the committee was not "necessary to fulfil its remit”.
She said: “After reviewing the material received from the Crown Office, the committee has unanimously agreed that the private communications within the material will not be published. These communications included numerous chains of private messages between different women in what we are clear were safe spaces for confidential support.
“The committee is clear that publication and further consideration of this material is not relevant to the committee’s work or necessary to fulfil its remit. We will not publish any of these messages as we are clear that we will not do anything that may cause further unnecessary distress to any women.
“We will not be commenting further to seek to limit further speculation on these messages.”
One senior source in the Scottish Government said the content of the messages “destroys” any accusation of conspiracy.
They said: "This destroys Alex Salmond’s conspiracy theory. Our political worst enemies have read these messages and concluded there is nothing to see here.
“This is the moment when people should recognise all they [the women] did was support each other through some difficult, emotional and traumatic times.”
Rape Crisis Scotland also published a statement from the women at the heart of the complaints against Mr Salmond wherein they state “not one” of the messages were relevant and that they only showed “bonds of friendship and support".
The joint statement criticised both the committee and the Crown Office for requesting the messages and ‘breaking the trust’ between victims and the prosecution service in providing them.
The statement says: “We are deeply disappointed that the committee saw fit to request messages between people identified by the police and the Crown as victims of sexual harassment, some of whose identities are protected by a court order.
"We have no doubt that members of the committee knew that vulnerable witnesses were involved when they made the request.
“We are also deeply disturbed that the Crown has felt it appropriate to break the trust we placed in it. Having been let down by the Crown Office, we feel this unnecessary act will have done serious damage to progress made over the last few years in sexual assault cases.
"We urge the Crown to consider the grave consequences of their actions and are actively considering further options.
“These messages, had they been published, would show clearly that there was no conspiracy between women, but bonds of friendship and support.
"It is impossible to counter claims of conspiracy by those who selectively choose messages, without any context. These are private and personal communications which should not need to be in the public domain to prove a theory false or for complainers to be believed.”
Mr Salmond and First Minister Nicola Sturgeon are set to give evidence to the committee in coming weeks.
Sources close to Mr Salmond argue that more messages outside of those provided by the Crown Office exist.
They told The Scotsman the real focus should be on messages involving the chief executive of the SNP, Peter Murrell, rather than from complainants and that other messages relevant to the committee are still held by the Crown Office.
It is also understood there is still doubt over whether Mr Salmond will appear in front of the committee on February 9.
The former first minister successfully challenged the complaints process used by the Scottish Government through judicial review.
It was conceded on the grounds of it being “tainted by apparent bias” and led to a legal bill of more than £500,000.
Mr Salmond was also acquitted of sexual offence charges in a trial last year.