In one Facebook post, Mr Bull linked to an article headlined: “International Red Cross report confirms the Holocaust of six million Jews is a hoax.”
Another appeared to imply Isis and Israel were working together.
Images of Mr Bull’s posts were reportedly circulated by local Labour members concerned about his candidacy.
The Peterborough Telegraph had first raised the issue with the party in mid-February, but news of Mr Bull's suspension only emerged this afternoon, two hours after the JC enquired about the case.
A Labour spokesperson said: “Alan Bull has been suspended from the party pending investigation.
“Labour takes all complaints of antisemitism extremely seriously, which are fully investigated and appropriate disciplinary action taken in line with our rules and procedures.
“Antisemitism has absolutely no place in the party, and we are committed to challenging and campaigning against it all its forms.”
Jennifer Gerber, Labour Friends of Israel director, said: “The suspension of Alan Bull is long overdue.
"It is beyond belief that someone who described the Holocaust a hoax, talked about Zionist control of the media and spewed conspiracy theories about Mossad killing JFK was allowed to become a Labour candidate in the first place and stay as a member long after his antisemitic posts were revealed.
"If Labour is to take antisemitism seriously, it must act immediately, not just after a damaging news story.”
Mr Bull told the Peterborough Telegraph the images had been “doctored” but declined to comment further when approached last month.
Meanwhile it has been claimed Jeremy Corbyn, the Labour leader, was a member of a second Facebook group which included links to antisemitic material.
The Guido Fawkes blog reported that Mr Corbyn was part of the History of Palestine group, in which members posted claims of a “Jewish centre where kidnapped Syrians are stripped of their entire bodies”.
Mr Corbyn and his party were heavily criticised earlier this month for their response to revelations he had been part of a secret antisemitic Facebook group for years before he became Labour leader.
In 2015, the JC revealed how Mr Corbyn had apparently used Facebook to back the painting of a mural in East London which was condemned for its antisemitic imagery.
It depicted a group of businessmen and bankers sitting around a Monopoly-style board and counting money. The mural was painted on the end wall of a private property, but was removed by local authorities after complaints from residents.
Mr Corbyn had offered apparent support to the artist three years earlier, writing on Facebook to ask why the image was being destroyed.
