The Panelbase survey for the Sunday Times found that 42% of respondents thought she should stand down now, while 45% said she should remain as First Minister at until at least the next Holyrood election, and 13% didn’t know.
The poll also found that the majority of those who expressed a view had safety concerns around the Gender Recognition Reform (Scotland) Bill, which was passed by MSPs in December and blocked by the UK Government.
The reforms would allow trans people to obtain a gender recognition certificate (GRC) without the need for a medical diagnosis.
The Bill would also allow 16 and 17-year-olds to apply for a GRC for the first time, and reduce the amount of time a person has to live in their acquired gender before they can be granted the document.
Of those who expressed a view, more than three-quarters (76%) said they think the Scottish Government’s plans to change the law on gender recognition would pose a safety risk in women-only spaces, such as changing rooms, hospital wards and prisons.
Just under a quarter (24%) disagreed.
Ms Sturgeon has said she intends to challenge the UK Government’s use of Section 35 to block the Gender Recognition Reform Bill from becoming law.
The survey, among 1,415 voters in Scotland, was carried out in the past week as the Scottish Prison Service published its review on the management of transgender prisoners in the wake of the Isla Bryson case.
Transgender prisoner Bryson, who was convicted last month of raping two women while still a man known as Adam Graham, was initially housed in an all-female prison before being moved to the male estate.
The poll also found that 15% of those who voted SNP at the last Westminster election said they wanted Ms Sturgeon to resign, as did almost one in five (19%) people who backed independence in the referendum in 2014.
Just over three-quarters (76%) of SNP voters and 72% of Yes voters said they wanted her to remain.
The poll found that finance secretary Kate Forbes, who is on maternity leave, was the most popular choice to succeed Ms Sturgeon, with 7% of respondents backing her.
An SNP spokesman said: “Poll after poll consistently shows Nicola Sturgeon is the most popular leader of any political party in Scotland – by a very long way – and this poll is no different.
“Polls also clearly show people across Scotland have no confidence in the Tory Party or their leadership – whether it be the unelected Tory Prime Minister Rishi Sunak or his lackey, Douglas Ross.”
He added: “Whether it be catastrophic economic policies or disastrous Brexit pursuits, Westminster is failing the people of Scotland and they know it.
“Families, businesses and industries across Scotland trust the SNP and Nicola Sturgeon to put them first and offer a better future as an independent country.”
A Scottish Conservative spokesman said: “Public discontent with Nicola Sturgeon is rising because she’s not focused on their priorities and her values are wrong.
“She is massively out of touch with Scottish people with her flawed gender self-ID policy.
“This has led to numerous U-turns, her chronic mishandling of the transgender prisoner row and her inability to admit that a double rapist is a man.
“To make matters worse, she chose to smear those who raised concerns over the safety of women and girls, rather than accept their legitimate fears.
“All the while, her government, which continues to be focused on its self-serving push for independence, is neglecting voters’ top priorities: the global cost-of-living crisis, a Scottish NHS on its knees and ending the damaging teacher strikes.”
A UK Government spokeswoman said: “The Secretary of State for Scotland has made an order under section 35 of the Scotland Act 1998, preventing the Scottish Parliament’s Gender Recognition Reform (Scotland) Bill from proceeding to Royal Assent.
“This was done after thorough and careful consideration of all the relevant advice and the policy implications.
“This legislation would have an adverse impact on the operation of Great Britain-wide equalities legislation.
“Transgender people deserve our respect, support and understanding.
“Our decision is about the legislation’s consequences for the operation of GB-wide equalities protections and other reserved matters.”