The First Minister was responding to news that Ruth Davidson's party had suspended Jane Lax, the treasurer of the Conservative Association in Moray, after she joined in cruel mocking of Ms Sturgeon's miscarriage in a Twitter discussion.
Jane Lax replied to an anonymous Twitter account suggesting that Ms Sturgeon's revelation of having a miscarriage in 2011 was 'fictional'.
Ms Lax wrote: "Is that when she dropped a book."
The First Minister revealed in a book extract released in 2016 that she had suffered a miscarriage in the run-up to the 2011 Scottish Parliament elections.
She told Bauer Media earlier today: "I absolutely think that it's right for her to be suspended - obviously these comments are hurtful, and not just hurtful to me and to people close to me.
"I've been contacted by women who have also suffered miscarriages and these kind of comments also stir up hurtful and painful feelings in others as well.
"I welcome the fact that she's been suspended - I don't want to talk too much about what she said because I don't want to dignify it with a response."
"I would say more generally that for anybody who finds their political disagreements with somebody leading them to make such offensive comments really has to take a long hard look at themselves and really think about what kind of person they are.
"Hopefully she will learn from this."
The Scottish Conservatives confirmed on Wednesday evening that Ms Lax had been suspended from the party pending an investigation.