Ms Sturgeon said the Foreign Secretary asked her about how to get into the magazine when they briefly met last year.
Earlier in the Tory leadership race, Ms Truss dismissed Ms Sturgeon as an “attention seeker”.
Ms Sturgeon was interviewed by LBC’s Iain Dale at the Edinburgh International Conference Centre during the city’s Fringe festival, where she described Boris Johnson as a “disgrace to the office of Prime Minister”.
Asked about Ms Truss’s comments about her, Ms Sturgeon said she initially thought “it was made up, it was a spoof.”
The First Minister then said she had met Ms Truss during an event at the Cop26 summit in Glasgow last year.
Ms Sturgeon said she had recently been interviewed by Vogue magazine before their encounter.
She told the audience: “That was the main thing she wanted to talk to me about, she wanted to know how she could get into Vogue – and she calls me an attention-seeker
“I said to her they came and asked me.
“I didn’t really mean to do this, but I said to her it hadn’t actually been my first time in Vogue, it had been my second time.
“It looked a little bit as if she’d swallowed a wasp.
“I’m sure she’ll be in Vogue before too long.”
She continued: “I remember it because there we were at the world’s biggest climate change conference in Glasgow, world leaders about to arrive
“That was the main topic of conversation she was interested in pursuing. And once we’d exhausted that it kind of dried up.
“I’m sure we’ll have many more conversations about many more substantive things.”
Earlier, Ms Sturgeon discussed her interactions with Boris Johnson.
Comparing him to his predecessor, she said: “I think perhaps uncharitably I described my conversations with Theresa May when she was Prime Minister, as being soul destroying.
“I look back somewhat fondly now on that.”
Ms Sturgeon said she and Ms May “differed massively” in their political beliefs but the former Prime Minister “took the job seriously”.
In contrast, she said her interactions with Boris Johnson were “one long bluster”.
She continued: “You know, he was a third Prime Minister I’ve dealt with as First Minister.
“It was literally like nothing I’ve ever dealt with before in terms of any senior politician
“You know, I’m going to be blunt here, he was a disgrace to the office of Prime Minister.”