The former home secretary had suggested the measure would form part of the new Criminal Justice Bill included in the King’s Speech.
It triggered a widespread backlash, including from Tory MPs, after she said being homeless was “a lifestyle choice” that should be stopped.
Downing Street said on Tuesday that her proposal had been ditched.
“It’s not going to be introduced in the Criminal Justice Bill,” the prime minister’s spokesperson said.
Appearing to confirm the plan earlier this month when it was reported by the Financial Times, Braverman tweeted: “We cannot allow our streets to be taken over by rows of tents occupied by people, many of them from abroad, living on the streets as a lifestyle choice.
“What I want to stop, and what the law abiding majority wants us to stop, is those who cause nuisance and distress to other people by pitching tents in public spaces, aggressively begging, stealing, taking drugs, littering, and blighting our communities.”
The shake-up has angered many right-wing MPs who believe the prime minister is attempting to move the party back towards the centre.
In a sign of the bad-blood between Braverman Sunak, the PM sacked her over the phone rather than in person and the pair are yet to exchange formal letters.
Braverman has been widely seen to be laying the groundwork for a Tory leadership bid should the government lose the next election.
Following her return to the backbenches, she said: “I will have more to say in due course.”