The cabinet minister, who has previously been a staunch supporter of the PM, also said she will put her name into the ring if there is a leadership contest.
Attorney general questions take place at 10am on Thursday in the Commons.
Braverman told Peston on ITV that Johnson had handled matters “appallingly” in recent days.
She said: “The balance has tipped now in favour of saying that the prime minister – it pains me to say it – but it’s time to go.”
On not resigning, she said: “My first duty is to the country, Robert, and as attorney I’m the senior law officer.
“And we’re in a crisis and I have statutory legal and constitutional duties…
“I don’t want to resign because I have that duty. We need an attorney in government.”
Asked whether she recognises that Johnson will likely sack her, she said: “That is his choice, and I will do whatever the prime minister asks me to do.”
The PM rejected calls to quit on Wednesday. He was later hit with the departure of a third cabinet minister – Welsh secretary Simon Hart – as well as Braverman’s demand.
The withdrawal of the attorney general’s support marks a significant shift by the QC, who was elected as MP for Fareham in May 2015 before being appointed as the top legal official by Johnson in February 2020.
She became the first cabinet-level minister to take maternity leave and was reappointed to her ministerial position in September.
During last month’s confidence vote, Braverman expressed hope the PM would win the poll with a large margin.
The Euro-sceptic had been a supporter of Johnson since her days as the chair of the Brexit-backing European Research Group.