The Commons Speaker also said in a speech that the only possible Brexit was one backed by MPs.
A new law, passed before the suspension of Parliament, forces the PM to seek a delay until 31 January 2020, unless a deal or no-deal exit is approved by MPs by 19 October.
The PM has said he would rather be “dead in a ditch” than ask for a delay.
Responding to Mr Bercow’s comments, Tory Brexiter MP Sir Bernard Jenkin said the role of the Speaker had become “irretrievably politicised and radicalised”.
Meanwhile, Downing Street has announced Mr Johnson will travel to Luxembourg on Monday to hold talks with European Commission President Jean-Claude Juncker, and the country’s prime minister Xavier Bettel.
Delivering a lecture in London, Mr Bercow said: “Not obeying the law must surely be a non-starter. Period.”
He said it would be a “terrible example to set to the rest of society”.
“Surely, in 2019, in modern Britain, in a parliamentary democracy, we – parliamentarians, legislators – cannot in all conscience be conducting a debate as to whether adherence to the law is or isn’t required.”
He called it “astonishing” that “anyone has even entertained the notion”.
“If that demands additional procedural creativity in order to come to pass, it is a racing certainty that this will happen, and that neither the limitations of the existing rule book nor the ticking of the clock will stop it doing so,” he added.
The new law could force a Brexit delay beyond the current 31 October deadline by requiring the prime minister to request an extension to the UK’s EU membership.
This would be done by making him write to EU leaders to prolong talks under Article 50 – the part of the EU’s Lisbon Treaty which sets out what happens when a country decides that it wants to leave the EU.
The law forcing the PM to seek a delay unless MPs vote for a deal or no deal received royal assent on Monday, the final day that MPs sat in this session.
Parliament was suspended – or prorogued – in the early hours of Tuesday and is not scheduled to return until 14 October.
Foreign Secretary Dominic Raab has said the government would abide by the law, but would “test to the limit” what it requires of ministers.
Sir Bernard, who chairs the constitutional affairs select committee in Parliament, said the Commons should “adapt itself” to a new role for the Speaker.
He accused Mr Bercow of launching a “personal attack” on the prime minister, insisting this would have been “unthinkable 10 or 15 years ago”.
The current position allows the occupant “unregulated and untrammelled power”, he told BBC Radio 4’s Today programme.
“It’s a kind of majoritarian dictatorship position,” he added.
Another Leave-voting Conservative MP, Michael Fabricant, said Mr Bercow had brought the office of Speaker into disrepute:
On Thursday, Mr Johnson insisted the UK “will be ready” to leave the EU by the current deadline without an agreement “if we have to”.
In response to the publication of the government’s Yellowhammer document, an assessment of a reasonable worst-case scenario in the event of a no-deal Brexit, Mr Johnson reiterated it was “the worst-case scenario”.
“In reality we will certainly be ready for a no-deal Brexit if we have to do it and I stress again that’s not where we intend to end up,” Mr Johnson said.
Mr Bercow has announced he will stand down as Commons Speaker and MP at the next election or on 31 October, whichever comes first.
No reason to be optimistic’
The Speaker’s warning came as the EU’s chief Brexit negotiator told political leaders in the European Parliament on Thursday that he could not say whether contacts with the UK government would result in a deal by mid-October.
Michel Barnier, in a speech to MEPs, suggested that negotiating a new withdrawal agreement remained uncertain despite discussions between Mr Johnson’s team and the EU.
“I cannot tell you objectively whether contacts with the government of Mr Johnson will be able to reach an agreement by mid-October,” he said.
“While we have previously reached an agreement, as far as we can speak, we have no reason to be optimistic.”
He added: “We will see in the coming weeks if the British are able to make concrete proposals in writing that are legally operational.”