Mr Murrell had been invited back to the committee after he was accused of giving testimony that is “clearly at odds” with other evidence given to the inquiry.
Jackie Baillie had also written to the Crown Office asking for an investigation into whether Mr Murrell had perjured himself in front of the committee.
Mr Murrell confirmed to parliamentary clerks on Monday he would not attend the session on Tuesday.
Reacting, Ms Baillie, Scottish Labour’s spokesperson on the committee, said: “It is very disappointing that Peter Murrell is not attending the committee tomorrow.
"He does have questions to answer and I hope he will make himself available in the very near future.”
Ms Baillie had previously written to the Crown Office demanding an investigation into Mr Murrell.
The allegation of potential perjury rests on his statement that no other messages relevant to the inquiry existed, something the committee believes to be false.
A conviction for perjury can lead to a prison sentence of up to five years or a fine.
Murdo Fraser, the Scottish Conservative spokesman on the committee, tweeted suggesting section 23 powers could be used to compel a witness to attend, adding: “Watch this space.”
In a separate statement, Mr Fraser said: “Peter Murrell’s refusal to reappear before the committee will only raise more suspicions about what he doesn’t want to answer about this case.
“The First Minister promised that the SNP Government would be open and transparent with this inquiry, but now the chief executive of the SNP can’t even bring himself to be questioned again.
“His previous appearance was littered with contradictory statements, which is why he should have been willing to clarify his evidence.
“Mr Murrell is showing complete contempt towards the committee and must make himself available for questioning as a matter of urgency.”
The Scottish Parliament’s committee is examining the botched handling of harassment complaints against Mr Salmond.
The former first minister was also acquitted of sexual offence charges in a trial last year.