The survey by the Conservative Home blog put the Scottish Tory leader at the bottom of a ranking of Mr Johnson’s cabinet ministers, with an approval rating of 14.8 per cent - a fall of nearly 30 per centage points from her rating of 42.8 per cent at the end of June.
Tensions between Ms Davidson and the Prime Minister have ramped up after he sacked one of her closest allies, David Mundell, as Scottish Secretary.
Ms Davidson then warned that she would not support a no-deal Brexit, which Mr Johnson says he will proceed with if the EU does not reopen the current agreement to scrap the Irish border backstop.
Conservative Home does not publish the number of participants that take part in its online surveys. Conservative Home, which is a popular forum for Tory activists and politicians, speculated that the fall in Ms Davidson’s popularity was “most likely fallout from her highly publicised split with the Prime Minister and hostility to no deal”.
The Scottish Tory leader has previously been touted by UK Conservatives as a possible future Prime Minister.
SNP MSP George Adam claimed the survey was Ms Davidson’s “latest humiliation”.
“Ruth Davidson has been utterly shown up by her colleagues in Westminster and the rest of her party, who seem determined to treat Scotland as an afterthought, and she has failed to make any impact since returning to Holyrood.”
Mr Adam went on: “Despite all the bluster from Scottish Tories, we know they will ultimately fall into line behind whatever disaster Boris Johnson drags us into.”