Smith, the corporation’s first Scotland editor, recently told of her “relief” at moving to the US to become North America editor due to the “bile” she received while in the Scottish role.
Speaking to the head of corporate affairs at BBC Wales Rhys Evans for an academic paper, the broadcaster said she had been subject to “misogynistic” ideas that she would follow the political ideology of her father – former Labour leader John Smith.
In one incident, she recalled, someone rolled down their car window and asked “what f****** lies are you going to be telling on TV tonight you f****** lying bitch?”
Smith said she was “demonised quite heavily… amongst certain parts of the population”, during her tenure, as the corporation came under scrutiny during the 2014 independence referendum.
Speaking to the PA news agency on Friday, the First Minister condemned “unreservedly” abuse that had come from those who share her political leanings.
SNP MSP James Dornan accused Smith of “imagining” the abuse, before walking back and eventually apologising for the remarks, while former SNP MP Phil Boswell accused her of being a “traitor”.
Ms Sturgeon said: “Some of it comes from people who profess to be on my side of the political debate and I condemn that unreservedly.
“I have no truck with anybody and actually don’t consider myself to have much, if anything, in common with anybody who would hurl abuse at Sarah Smith or any other journalist.
“Nobody should put up with that abuse, no journalist whatever their gender should put up with abuse for doing their job.
“Journalists are an important part of the fabric of our society and politicians are rightly scrutinised and held to account by journalism.
“So nobody should put up with that kind of abuse.”
She added that abuse suffered by journalists including Smith should not be “weaponised” by other politicians for party reasons, after members of the Scottish Tories called on her to do more the stifle the issue in her own ranks.
“I’ve seen comments today – and I’m not going to name any names – from other elected politicians, I don’t know whether they’re meaning to suggest this, but almost suggesting that the unacceptable abuses that Sarah Smith has had is somehow my fault and my responsibility,” she said.
“I’ve got a responsibility to call it out, of course I have, but actually, instead of politicians on the other side of the debate saying it’s my fault when it is coming from people professing to be on my side or vice-versa, we should all come together to marginalise it and force it out of politics completely.
“I don’t hold the leaders of other political parties responsible for a minority who abused me and so we need to stop seeing this as something to be weaponised against each other and actually be prepared to call it out, but call it out from a position of unity and a position of solidarity and common cause.”