Polling company YouGov asked 4,112 UK adults on Tuesday whether Mr Johnson should quit after his prorogation of Parliament was found to be unlawful, with 43% saying he should, compared with 39% who said he should not.
The remainder said they did not know.
The majority of Tories (56%) and Leave voters (57%) questioned said they disagreed with the court's ruling, while 73% of Labour voters and 78% of Remain voters agreed with it.
YouGov also found that 55% of people in Scotland believe Mr Johnson should resign, while just over a quarter said he should not and 19% said they did not know.
68% of people in Scotland said the Supreme Court was correct in its ruling against Mr Johnson.
SNP Westminster leader Ian Blackford said: "This YouGov poll is yet another nail in the coffin of Boris Johnson's premiership.
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"His decision to shut down Parliament in an attempt to force through an extreme Tory Brexit did not stand up in court and it's clear it will not wash with people across Scotland and the UK – with an overwhelming majority agreeing he should resign.”
Meanwhile, MPs are preparing to return to Westminster after the bombshell legal ruling.
The PM will fly back from New York into a political storm as furious opposition parties attempt to hold him to account over his Brexit plans.
Downing Street insisted there was no question of him standing aside, despite the Supreme Court ruling.
Mr Johnson updated Cabinet ministers on the ruling in a conference call on Tuesday during which Commons Leader Jacob Rees-Mogg reportedly said the Supreme Court judgement amounted to a "constitutional coup”.
Mr Johnson also spoke to the Queen after the verdict, according to a Government source who would not comment on whether he apologised to the monarch for having advised her to suspend Parliament for five weeks.
The court's ruling that the prorogation was "void and of no effect" meant there was no need for the Government to formally recall Parliament.