Kathleen Leslie has previously apologised for outbursts, including calling millionaire Weir family "uneducated fat f******."
The Daily Record reports that Kathleen Leslie was removed from the teaching register after her comments.
An SNP spokesperson told the paper: "It is beyond belief that the Tories think someone struck off the teachers register is suitable to stand for MP.
"We know the Tories have questionable taste in candidates, but they are scraping the bottom of the barrel."
The paper reports that Leslie, who is a councillor in Fife, previously wrote of Sturgeon: "Wee Jimmie Krankie is a drooling hag. She's a walking horror show. That wee fish wife was there!? at taxpayers' expense no doubt."
A Scottish Conservative spokesman said: "Kathleen has apologised for the comments she made. She has a great record as a local councillor in Fife and has the party's full support."