Mollie Collins, who sits on the party's executive board in the south west and was chair of South Dorset Labour Party until last month, shared an article on Facebook that suggested the Nazi murder of six million Jews was a "lie".
She also posted a number of articles and videos about the Rothschild family that were based heavily on antisemitic conspiracy theories.
The Independent understands that she has been suspended by the party pending an investigation.
Ms Collins, who unsuccessfully stood as a Labour council candidate in May, shared an article in 2016 titled "The Realist Report: How the 'Holocaust' was faked".
The post, which has since been deleted, linked to an article claming that the death of six million Jews at the hands of the Nazis was "laughable" and "the biggest lie ever foisted upon humanity".
It said: "The very idea that the Germans organised and executed a complex conspiracy involving 'homicidal gas chambers' and other barbaric, sadistic forms of mass murder designed to exterminate European Jewry during WWII is laughable on its face when you stop and objectively think about it."
The article claimed that inmates of Nazi concentration camps had been "well-cared for...well-fed, well-provided for", with access to "medical treatment and entertainment". Prisoners were allowed to "attend concerts, organise plays, make music and play sports", it wrongly alleged.
The article also quoted approvingly from Adolf Hitler's Mein Kampf, saying the Nazi leader had offered "profound insights" about Jewish people.
Other posts shared by Ms Collins focused on the Rothschild banking dynasty, which is one of the most common subjects of antisemitic conspiracy theories.
One article claimed that the Jewish family was behind the 9/11 attacks, while another suggested they had brought down Malaysian Airlines flight MH370, which is still missing.
Other posts shared on Ms Collins' Facebook page suggested that Hillary Clinton worked for the Rothschilds, and that the dynasty controlled much of the media.
Ms Collins also shared a post saying a satirical article alleging that the USA had been "sold" to five wealthy Jewish families was "spookily accurate" because they "really do own and control" the US government.
A Labour Party spokesperson said: “The Labour Party takes all complaints of antisemitism extremely seriously, which are fully investigated in line with our rules and procedures and any appropriate disciplinary action is taken. We cannot comment on individual cases.”
Ms Collins has been contacted for comment.