Ken MacBrayne has been told he will receive no more support from the party after a string of posts came to light.
The 72-year-old is seeking election to Western Isles Council.
The Tories said the comments were "totally unacceptable" and said Mr MacBrayne was "no longer a member".
However, he will still appear on the ballot for the Benbecula and North Uist ward on 4 May as the nomination list is finalised.
Publicly viewable posts on social media platforms by Mr MacBrayne included insults directed at Ms Sturgeon and calls for her to be physically gagged.
He also shared posts by right-wing group Britain First calling for immigrants and asylum seekers to be denied benefits and predicting a religious war in the UK and Europe.
An SNP spokeswoman said: "Mr MacBrayne's comments are extremely offensive, with rants of this nature completely inappropriate from someone standing for public office.
"The disturbing, extremist views include what is essentially neo-Nazi propaganda gloating about a coming race war from a self-proclaimed 'resistance' group.
"It is staggering that this bile is coming from a Tory candidate."
A Scottish Conservative spokesman said: "These comments are totally unacceptable, and the party have informed the candidate that he shall be receiving no further support for his campaign.
"The party has also suspended Mr MacBrayne, and he is no longer a member."
A Conservative candidate for May's council elections has been suspended from the party after posting "extremely offensive" online comments about First Minister Nicola Sturgeon.