It comes as Police Scotland is currently assessing a complaint after footage showed her apparently breaching Scotland’s Covid face mask law on the council election campaign trail.
A video posted on social media appears to show Scotland’s First Minister not wearing a mask during a visit to a barber’s in East Kilbride, South Lanarkshire, on Saturday.
The event took place before the legal requirement to wear a face covering was scrapped from Easter Monday onwards.
Speaking on BBC Good Morning Scotland this morning, Professor Leitch said the First Minister’s actions were “actually what we’re asking people to do”, adding the First Minister realised within “a matter of seconds” she had to put a face covering on.
Defending Ms Sturgeon, Professor Leitch said: “’I’ve done that too, I’ve got up from the dinner table quite recently out for a meal, gone to the bathroom and halfway there you realise, ‘Oh, I need to put my face covering on’.
"Because it does still feel like a slightly odd thing to have to do. My understanding of that incident – I haven’t spoken to the First Minister today, I imagine I’ll speak to her later – my understanding is it was a matter of seconds, she realises the place is crowded, puts her face covering on, which is actually what we’re asking people to do.
"The guidance says if you are in a crowded area, inadvertently or deliberately, then put a face covering on and that will protect you and others.”
Criticising Professor Leitch, The Scottish Conservatives have said his remarks were “inappropriate” for him to make as a civil servant.
Scottish Conservative MSP, Craig Hoy said: "It is inappropriate for a civil servant to defend Nicola Sturgeon in this way. These kinds of questions should be left to politicians to answer. Instead, SNP ministers are in hiding and Jason Leith is blurring the lines between ministers and government officials.”
The Scottish Conservatives also accused Professor Leitch of “misrepresenting” the Covid laws that were in place at the time.
Mr Hoy added: "Face mask use was still in law until today but Mr Leitch backed up Nicola Sturgeon's excuse that she only had to put the mask on when in a crowded space.
"If the SNP had listened to us weeks ago and changed face mask rules from law to guidance, he and Nicola Sturgeon would have been correct.
"But they failed to do this and Mr Leitch should not be confusing the public, or doing the SNP's job for them, by trying to defend Nicola Sturgeon in this manner."
An SNP spokesman said: “The First Minister was invited into the barber’s during an outdoor visit on the street.
“Within a few seconds, she realised she hadn’t put her mask back on and immediately put it on.”
Those who breach the face covering rules can face a fine of up to £60.