Noel Dolan said Permanent Secretary Leslie Evans had to go for the “good” of the Scottish civil service.
Ms Evans had led a Holyrood inquiry in late 2018 into allegations made against Mr Salmond - but the exercise was later branded unlawful and biased following a legal challenge in the Court of Session, a decision that cost taxpayers £600,000.
The botched investigation was later overshadowed when the former SNP leader was arrested in early 2019 and charged with 13 counts of sexual assault.
Mr Salmond was eventually cleared on all counts at the High Court in Edinburgh on Monday.
Mr Dolan, who served as Ms Sturgeon’s most senior advisor when was deputy first minister, told the Daily Record: “The original inquiry was a mess. Leslie Evans should stand down.
“For the good of the Scottish civil service, she should go.”
He added: “As she cost the Scottish taxpayer a large amount of money, she should have gone in 2019.”
Meanwhile, Mr Salmond is expected to outline potentially devastating allegations of a political conspiracy against him if called to give evidence at a Holyrood inquiry later in the year.
The former SNP leader is expected to be questioned as part of a review of how the Scottish Government handled complaints against him.
The committee of MSPs, led by deputy presiding officer Linda Fabiani, will examine why a complaints procedure was changed just weeks before allegations were made against Mr Salmond.
A decision was made to allow retrospective grievances to be aired against ex-ministers.
The fall-out from Mr Salmond’s acquittal has already seen one senior MP call for an independent inquiry into how her party handled the allegations.
Joanna Cherry also called for the former party leader to be readmitted to the SNP “without delay”.
And a former depute leader of the SNP said there is “compelling evidence” that Alex Salmond was the victim of a political set-up.
Jim Sillars welcomed the jury’s decision to clear the former First Minister of all charges at the High Court in Edinburgh yesterday, but warned a number of senior Nationalists would now be “quaking in their shoes” at the verdict.