The YouGov survey for the pro-union Scotland in Union campaign group found 32% of Scots think the country should wait for the Brexit deal before a repeat of the 2014 ballot while 25% do not want another vote on independence until at least 2030.
A further 17% said Scotland should never have another referendum while 16% want a vote as soon as possible, 9% said they did not know and the remainder said they did not agree with any of those views.
The UK Government’s plan for leaving Europe is not yet clear, although Brexit Secretary David Davis has suggested it could begin formal negotiations early next year.
Ms Sturgeon has said she would consider calling a second referendum if the UK’s position emerges as unacceptable to Scotland’s interests.
Alastair Cameron, of Scotland in Union, said: “We know the EU referendum result has left many Scots disappointed and some people are calling for the debate on Scottish independence to be re-opened.
“This poll shows that Scotland does not want to rush into another referendum and one in three Scots want to see what Brexit means before deciding on our future.
“We believe people deserve to know what this new landscape will mean for trade, for currency and for our borders.
“Importantly, before dragging Scotland into another referendum, we need to hear from those proposing Scottish independence how we would deal with Scotland’s £15 billion deficit.”
The poll of 1,006 people - carried out between July 20 and 25 - also found that 46% of people think another independence referendum would have a negative impact on the economy while only 22% think it would be positive.
Asked to rank their top priorities for the Scottish Government, the NHS, the economy and working with the UK Government on an EU deal came top ahead of getting a separate EU deal for Scotland and holding another referendum on Scottish independence.
Mr Cameron added: “These new figures show that the people of Scotland believe premature talk of a second referendum is bad for business and they want politicians in Holyrood to be focusing on the NHS and the economy.”
Scottish Conservative constitution spokesman Adam Tomkins said: “This is more evidence that the SNP’s headfirst lunge towards a second referendum following Brexit is not what the people want.
“Nicola Sturgeon should be working with the rest of the UK to get the best deal for Scotland.”