Ms Sturgeon made the statement at the coronavirus update briefing on Wednesday, after UK Government Health Secretary Matt Hancock said earlier in the day that he would do the same thing.
Responding to questions from journalists on whether she would follow suit, the First Minister said: “We won't leave any stone unturned in terms of trying to get maximum number of people coming forward and taking this vaccine, and if me getting it done on live television can help with that I will do that, happily.”
However Ms Sturgeon added that a politician may not be the best person to front such a campaign.
She said the government is considering engaging celebrities, perhaps including Andy Murray, to act as ‘vaccine ambassadors’ to convince people to get the shot.
"We will certainly be considering an overall campaign to encourage people to come forward and of course we will consider using, if they are willing, well known and well respected people,” she said.
“I was asked this question on television earlier in the week and it was put to me that Andy Murray might be one. We’ve not had conversations to the best of my knowledge with Andy Murray but I’m sure people like that, who the vast majority of Scotland have huge respect for, could be helpful in this.”
It comes after reports in England suggested that Marcus Rashford and members of the Royal Family may be included in a list of celebrity vaccine 'ambassadors’.
Well-known doctors and Instagram influencers may also be under consideration.
Matt Hancock appeared on Good Morning Britain on Wednesday morning, where he said he would take the vaccine on live television with Piers Morgan to reassure people it is safe.
He said he would need to get the stunt approved as he is not in a priority group.
"But if we can get that approved and if people think it’s reasonable then I’m up for doing that… if that can persuade anybody else that they should take the vaccine, then I think it’s worth it,” he said.