The culture secretary retweeted an image of the PM depicted as Julius Caesar about to be stabbed in the back by Mr Sunak, in the role of Brutus.
Greg Hands said it was "dangerous", while Sir Robert Buckland said it was "not just incendiary - it's wrong".
An ally of Ms Dorries said it was "obviously a satirical image".
Shortly before sharing the picture that was posted by another account on Twitter, Ms Dorries also wrote that Mr Sunak had "stabbed Boris Johnson in the back".
Mr Hands said he was sure Foreign Secretary Liz Truss - who is being backed by Ms Dorries - would "disown this kind of behaviour".
The business minister, who is a supporter of Mr Sunak said: "It's not even a year since the stabbing of Sir David Amess at his Southend constituency surgery. It is very, very bad taste - dangerous even.
"I do find it distasteful and less than a year after the stabbing."
Fellow Conservative MP Sir David was stabbed to death by Islamic State fanatic Ali Harbi Ali in Essex in October last year. Ali has since been jailed for life for the murder.
Former Northern Ireland Secretary Brandon Lewis, who also backs Ms Truss, said it was "certainly not the kind of thing I would tweet".
He added it was "not a comment from Liz's team, her campaign or Liz herself, adding: "Nadine speaks for herself. That is not a position that Liz would take."
The death of Julius Caesar, the iconic general whose murder by fellow politicians paved the way for the establishment of the Roman Empire nearly 2,000 years ago, is sometimes used as a metaphor for betrayal, political or otherwise.
Welsh Secretary Sir Robert Buckland, another supporter of Mr Sunak, also criticised Ms Dorries' actions, telling BBC Radio Wales that the use of "that sort of imagery and narrative is not just incendiary, it's wrong".
He also said people engaging in personal attacks "should wind their neck in and let people talk about the issues rather than the personality".
Senior Conservative MP Simon Hoare also denounced her actions as "divisive, disingenuous & disturbing", describing her actions as "harmful to the party".
"Remembering, with respect, our fallen colleagues David Amess and [murdered Labour MP] Jo Cox. The injured Stephen Timms. I will just leave it there," he wrote on Twitter.
Responding to the criticisms, an ally of Ms Dorries 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. Some people of course will want to be wilfully offended…"
The sharing of the image comes as Ms Dorries, a consistent and vocal supporter of Boris Johnson, has ramped up her fierce criticism of Mr Sunak in recent weeks.
In an article in the Mail on Sunday, she accused the former chancellor of "planning a coup" that was "Tudoresque in its degree of brutality".
Mr Sunak was one of the first and most senior members of the cabinet to resign following the controversy over the government's response to allegations that former Tory MP Chris Pincher groped two men, which led to the resignation of Mr Johnson.
Ms Dorries also defended an earlier tweet criticising Mr Sunak's "£450 Prada shoes" and comparing them to Ms Truss's "£4.50 earrings" purchased from budget jewellery shop Claire's Accessories.
She denied her comments were "anti-aspirational" and said her intention was to "alert Tory members not to be taken in by appearances".
Ms Dorries wrote: "The assassin's gleaming smile, his gentle voice and even his diminutive stature had many of us well and truly fooled."
She argued she was criticising his "lack of self-awareness for wearing such expensive clothes" during a visit to Teesside last week, which she said was one of the "most socially deprived towns in the North of England".
The culture secretary also accused Mr Sunak of refusing to sign off a review of the BBC licence fee in government but later announcing a review of the BBC licence fee as a candidate.
Watch: Why Nadine Dorries called out Rishi Sunak's suit