A ComRes survey for the Sunday Express found that 53% of people were against the former Foreign Secretary being punished for his comments, while 40% said he deserved to be disciplined.
Mr Johnson’s comments, in which he described Muslim women in face-covering veils as looking like letterboxes or bank robbers, have sparked infighting in the Conservative Party.
The Uxbridge MP is facing an investigation by an independent panel following complaints that his comments on women who wear burkas breached the Conservative Party’s code of conduct.
The ComRes poll was released as Mr Johnson returned to the UK from a holiday in Italy.
Mr Johnson made no comment to waiting reporters as he arrived back at his Oxfordshire home on Saturday evening, but is expected to break his silence in his regular Monday column in the Daily Telegraph, where his controversial comments were first printed six days ago.
Amid complaints from supporters of an attempt to gag Mr Johnson, the ComRes poll found that 60% of respondents believe that rights to free speech are being weakened, against just 5% who said they were strengthening.
Support for Mr Johnson was markedly higher among older generations, with 77% of over-65s and 63% of 55-64 year-olds saying he should not face discipline, while 62% of 18-24 year-olds and 55% of those in the 25-34 age-group saying he should.
The poll found that Theresa May remains voters’ preferred leader of the Conservatives, by a margin of 26% to 24% over Boris Johnson, with 42% opting for “neither”.
The row has sparked infighting in the Conservative party, with Tory MP Andrew Bridgen, a supporter of Mr Johnson, warning of “open warfare” in the Conservative Party if he is suspended in such a way that he cannot take part in a future leadership contest.
He told the Sunday Express: “If Boris is suspended it will be open warfare in the Conservative Party. If Theresa May dares engineer a leadership contest while Boris is suspended it will be World War Three.”
Brexit-backing MP Jacob Rees-Mogg has branded the investigation launched into Mr Johnson’s remarks as a “show trial” motivated by Mrs May’s personal rivalry with her former Cabinet minister.
The Sunday Times reported that four Cabinet ministers had privately expressed dismay at the handling of the case.
Far-right US activist Steve Bannon, who was in contact with Mr Johnson during his recent visit to the UK, has urged him not to “bow at the altar of political correctness” by apologising, telling the Sunday Times that Mr Johnson had “nothing to apologise for”.
Former first secretary of state Damian Green said he feared Mr Johnson was “being turned into a martyr by the alt-Right”, which would be “a disaster for him and the Conservative Party”.
Writing for the Mail on Sunday, he said: “I am particularly concerned by reports that President Trump’s sacked adviser Steve Bannon is forming a Europe-wide far-Right campaign group – and has been in touch with Boris.
“I hope that no Conservative politician, including Boris, is taking advice from him about how the Conservative Party should behave.”