Jane Lax, who the Daily Record reported was the treasurer of the Conservative Association in Moray, replied approvingly to a tweet that suggested that Ms Sturgeon's revelation of having a miscarriage was 'fictional'.
A tweet from an anonymous account shared a story regarding the First Minister's comments about the misogynistic abuse that she receives on Twitter and other social media networks, commenting 'the GERS figures must be imminent', a reference to the economic report on Scotland's finances that was unveiled yesterday.
Another anonymous account replied to that tweet, writing: "Has she mentions (sic) her fictional miscarriage yet?"
Ms Lax, who tweets as 'the SNP don't speak for me', then replied to both accounts writing: "Is that when she dropped a book."
This was an apparent reference to the comments that Ms Sturgeon made to writer Mandy Rhodes in 2016, when she revealed that she had suffered a miscarriage in the run up to the Scottish Parliamentary elections in 2011.
It was revealed in the Sunday Times as part of an extract from a book on SNP leaders which Ms Rhodes contributed to.
A spokesman for the Scottish Conservative told The National: “These comments are unacceptable. Her membership will be suspended pending a disciplinary procedure.”
SNP sources told the Record that Ms Lax should be suspended, while senior party councillor Mhairi Hunter wrote on Twitter: "Blimey I didn't realise @janela_X was actually a Tory party office-bearer. Glad to see her suspended."
Ms Lax was at the centre of controversy in May when she was featured on a BBC Question Time recording in Elgin, with accusations she was a 'Tory plant'.