Councillor Paul Nickerson, a Conservative who sits on East Riding of Yorkshire Council, apologised and deleted the tweet, but also claimed that it was posted by a friend who had access to his account.
Councillor Jonathan Owen, leader of the Conservative Group, said he had been suspended from the group with immediate effect for the “inappropriate and offensive” post.
The image showed the former Labour leader holding a wreath next to the taxi which was blown up outside Liverpool Women’s Hospital, shortly before 11am on Remembrance Sunday.
It appears to make reference to Mr Corbyn’s decision to attend a ceremony in Tunisia, when a wreath was laid in memory of some people accused of the 1972 Munich terror attack.
Councillor Owen, who is also leader of the council, said: “I have suspended him from the East Riding of Yorkshire Council Conservative Group with immediate effect and an investigation will now take place.
“All people in public life, irrespective of politics, should be united in condemning the terrorist attack that took place outside the Liverpool Women’s Hospital on Remembrance Sunday.
"It is not the time for inappropriate remarks, however intended, and they will not be tolerated in this Conservative Group.
“Residents should expect their elected representatives to act in an appropriate manner at all times.”
Councillor Nickerson said the Conservative Group "have no alternative but to investigate" and he will co operate fully.
He said: "Some of my social media accounts on my phone were compromised by friends without my knowledge as a prank. Unauthorised posts where deleted as soon as I could, but this particular message and a few others was re-posted to a larger group of social media users who continued to comment on it.
"I also want to apologise to people who were offended by that content – we should all work closely for a decent and respectful dialogue and cross party approach to solving people’s issues which, if you review my online output, you will see I try to consistently do."
He added: "I remain a councillor and will be working hard in my ward over the coming days supporting local residents.”
Emad Al Swealmeen, 32, who detonated a homemade bomb inside the vehicle in Liverpool, died at the scene but the driver, named locally as David Perry, survived and he has been discharged from hospital.
Police, who are being assisted by MI5 in the investigation, said “significant progress” had been made but it could take “many weeks” before they fully understand what happened.
The incident has been declared a terrorist attack and the UK terror threat level has since been raised from substantial to severe, meaning an attack is “highly likely” rather than “likely”.
It is understood that an Islamist plot is one line of inquiry but investigators are keeping an open mind and the motivation is yet to be established.
Assistant Chief Constable Russ Jackson, from Counter-Terrorism Police North West, previously told journalists the explosive device had been “manufactured” and the force’s assumption was that it was built by Al Swealmeen.
The probe is examining, among other possibilities, whether the main charge on the device failed to explode and is looking at if the homemade explosive TATP was used.