Sturgeon has said a second referendum was needed because of Scotland's opposition to Brexit, but the study found that rising euroscepticism in Scotland could undermine her argument.
Two other polls also published on Wednesday showed similar levels in favour of independence, although the support was broadly similar to previous comparable polls.
The Scottish National Party (SNP) leader on Monday announced she would be seeking authority from the Scottish parliament next week to hold a second referendum on leaving the United Kingdom.
This would ideally take place before Brexit, she said, as Prime Minister Theresa May prepares to start the two-year process of leaving the EU later this month.
The ScotCen long-term social attitudes study found that 46 percent of Scots now back independence, the highest level since the survey began in 1999.
"Overwhelming support for independence among younger voters might mean there is majority support for independence in future," it said.
But the survey, conducted between July and December last year, also found rising levels of euroscepticism, from 40 percent in 1999 to 67 percent last year.
"High levels of euroscepticism in Scotland mean focusing on EU membership may not be the best way to swing voters in favour of 'Yes'," it said.
Two other opinion polls by YouGov and Survation, meanwhile found that 43 percent and 47 percent of voters respectively would back independence, once the undecideds were excluded.
A YouGov poll in December had put independence support at 44 percent, while a Survation survey in September also showed a level of 47 percent.
May has yet to agree to the referendum, but noted that the European Commission had said Scotland would have to reapply for EU membership if it left the UK.
"Scotland will be leaving the European Union, it will leave the European Union either as a member of the United Kingdom or were it independent," she told MPs.
'We will have our say'
May initially rejected the idea of a second vote as "divisive", less than three years after Scots voted by 55 percent to reject independence in September 2014.
Angus Robertson, the SNP's most senior figure in the British parliament, told The Guardian newspaper that a referendum could be avoided if Scotland was allowed to stay in the EU single market.
But in testy exchanges in the House of Commons, he warned that time was running out.
He said May must agree her plan for Brexit with Scotland before she triggers Article 50 of the EU's Lisbon Treaty, starting a two-year countdown to leaving, by her deadline of the end of March.
"If she is not prepared to negotiate on behalf of the Scottish government and secure membership of the single European market, people in Scotland will have a referendum and we will have our say," Robertson said, sparking deafening cheers and jeers from MPs.
May told him she would remain in discussions with Sturgeon's government -- but rejected comparisons between Britain's move to end 43-years of EU membership, and Scotland's bid to leave the UK.
"We have been one country for over 300 years. We have fought together, we've worked together, we've achieved together," she told MPs.
"And constitutional game-playing must not be allowed to break the deep bonds of our shared history and our future together."
Sturgeon on Tuesday used Twitter to question May's mandate for Brexit, noting that she took office after the referendum "and is not yet elected by anyone".
May responded Wednesday with a subtle dig, noting last year's Scottish election in which Sturgeon "was returned as the first minister of a minority government".
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