The outgoing SNP leader described the move as being "part and parcel of the next phase of life".
It comes as she prepares to leave office after more than eight years at the helm of the Scottish Government.
Friend Ricky Bell said the lessons are a signal Ms Sturgeon is preparing for life after being First Minister.
Speaking to the BBC's Nicola Sturgeon Podcast, he said: "Anyone who knows Nicola knows she has been signalling for a wee while she was likely to go.
"And I think the big thing was she said she was taking driving lessons.
"You don't need driving lessons if you are going to be chauffeur driven about as the First Minister."
He added: "She said to me many years ago she didn't want to sit her driving test in case she failed, because up until that point in her life she had never failed an exam."
Ms Sturgeon told the podcast the driving lessons are "in the early stages".
She said getting behind the wheel is about "achieving a bit of personal freedom that I have chosen not to have to the same extent" while pursuing a political career.
"It's just part and parcel of the next phase of life," Ms Sturgeon added.
The Nicola Sturgeon Podcast will be available from Monday March 27 - the same day the new SNP leader is announced.