The picture has Johnson’s and the former chancellor’s faces imposed onto those of Roman leader Julius Caesar and one of the men who conspired against and killed him, Brutus.
The retweet by Dorries has been branded as “dangerous” by a fellow Conservative MP, especially after the fatal stabbing of Southend MP Sir David Amess.
What did the Conservative MP say about the retweet?
Greg Hands, who is backing Mr Sunak in the Tory leadership race, told Sky News the social media post was "appalling", especially after the fatal stabbing of Southend MP Sir David Amess in his constituency last year.
He said: "It is not even a year since the stabbing of Sir David... so I think this is very, very bad taste, dangerous even.
"I do find it distasteful and I do find it, less than a year after the stabbing of our colleague, in very, very poor taste, even verging on dangerous."
What was said in support of her?
An unnamed ally of Ms Dorries, who is backing Liz Truss in the leadership race, said: "It’s quite obviously a satirical image of Brutus and Caesar which has been clearly photoshopped to provide political commentary.
"There were similar cartoons involving [Michael] Gove in 2016.”
The ally added: “Some people of course will want to be wilfully offended."
The culture secretary has been a staunch defender of the prime minister and a fierce critic of those who contributed to his downfall.
It is not the first time she has caused controversy on social media.
She recently tweeted on the social media platform about the price of Mr Sunak’s suits, compared to the foreign secretary’s earrings from Claire’s Accessories.
She also wrote a damning piece in Saturday’s Daily Mail, accusing Mr Sunak of "planning a coup for a very long time" and saying she commented on his dress sense to "alert Tory members not to be taken in by appearances in the way that happened to many of us who served with the chancellor in Cabinet".
Ms Dorries added: "The assassin’s gleaming smile, his gentle voice and even his diminutive stature had many of us well and truly fooled."
What has been said about her controversial tweets?
Mr Hands said the increasingly bitter contest to become the next prime minister of the UK needed to be "fought on the issues and on the leadership qualities" of the two candidates, rather than insults.
Former Northern Ireland secretary Brandon Lewis, who is backing Ms Truss in the campaign, said the post did not represent the foreign secretary’s views.
He told Sky News: "It’s certainly not the sort of thing I would tweet."
He said Ms Dorries is "well-known for having strong views on things" and "speaks for herself".
But added: "I think we have all got to make sure that we remember we are one party, we come back together, we work together.
"We will have different views and the whole point of the leadership campaign is that both the candidates and their teams outline their differences of opinion so that the members can then choose who they think is the best person to lead our party and to lead our country."
Fellow Sunak supporter and Welsh Secretary Sir Robert Buckland also condemned the retweet, telling BBC Radio Wales: "I think that sort of imagery and narrative is not just incendiary, it’s wrong.
"I think it’s time for those who think that an argument about Prada shoes or earrings is more important, for instance, should wind their neck in and let people talk about the issues rather than the personality."