His refusal to back Ms Braverman comes as she faces mounting pressure to quit having been accused of inciting a mob of far-right protesters to descend on London and attack police on Armistice Day.
There has been speculation Mr Sunak will carry out a ministerial reshuffle, which could see her moved, but not before next week’s Supreme Court ruling on the Rwanda deportation policy which she has championed.
Asked about a potential reshuffle, Mr Shapps told Sky News: “The makeup of the cabinet is entirely a matter for the prime minister. He will decide that in his own time.”
Pressed on whether Ms Braverman would be home secretary this time next week, he said: “As you and I know well, a week is a long time in politics and I never make predictions about these things.”
Ms Braverman will lay a wreath at the Cenotaph in London on Sunday morning, having remained silent on Saturday’s demonstrations so far.
In a post on X, formerly Twitter, she said: “This morning I will be attending the National Service of Remembrance at the Cenotaph, paying my respects to our fallen heroes.
“We must honour them and the veterans who survive for the sacrifices they made so that we may live safe and free.”
Her appearance comes after a mass rally of around 300,000 pro-Palestinian demonstrators in London passed off without major incident on Saturday while more than 100 far-right thugs who turned up to confront them were detained by police after a series of violent clashes.
Mr Shapps denied that ministers were partly to blame for the chaos that unfolded despite Ms Braverman talking about “pro-Palestinian mobs” in the run up to the Armistice Day commemorations.
He said that “the people who were going to come and disrupt this weekend had already said they were going to do it”.
“Some people just turned up determined, by the way nothing to do with what the home secretary said, having already said they would be here doing these things to disrupt things here at the Cenotaph,” he added.
Labour leader Sir Keir Starmer, mayor of London Sadiq Khan, Scottish first minister Humza Yousaf and a slew of senior Tories blamed Ms Braverman for the violence that erupted, calling for Rishi Sunak to sack her.
Mr Sunak has so far maintained confidence in his home secretary, even after a week in which ministers distanced themselves from her claims that homelessness is a “lifestyle choice”.
Labour leader Sir Keir has accused Ms Braverman of “demeaning the office” of home secretary with her remarks in the run up to Remembrance Weekend.
Sir Keir said: “Few people in public life have done more recently to whip up division, set the British people against one another and sow the seeds of hatred and distrust than Suella Braverman. In doing so, she demeans her office.
“She also sets her face against the very values that Britain has fought for: values that the rest of the country will pay tribute to this weekend.”
This morning I will be attending the National Service of Remembrance at the Cenotaph, paying my respects to our fallen heroes.
We must honour them and the veterans who survive for the sacrifices they made so that we may live safe and free. pic.twitter.com/ewBpyEvc5z
— Suella Braverman MP (@SuellaBraverman) November 12, 2023
It came as Tory grandee Dominic Grieve repeated his call for Ms Braverman to quit.
The former attorney general told Sky News the home secretary showed she was “incapable of understanding her duty” to maintain the right to demonstrate under the rule of law. “She should resign,” he added.