The SNP leader and First Minister told the BBC's Andrew Marr Show it would be "wrong" otherwise given last year's "No" vote.
Speaking ahead of next week's SNP conference, Ms Sturgeon was asked about the prospect of going to the polls again to break-up the union.
She said: "It boils down to public opinion. If there's no shift in public opinion then I think it would be wrong to propose another referendum, but equally if we do see a sustained shift in public opinion it would not be right for anyone to rule it out."
The party has said it will map out a time-table for another referendum in the manifesto for the Scottish Parliament elections next year.
But she warned if Scotland votes to stay in the EU in the in-out referendum before 2017, but the UK withdraws, that is a "case apart".
She said that "so fundamentally changes the nature of the UK" that there would be "demand for another referendum and those circumstances would perhaps be unstoppable".
The party has previously said a "material" change in the circumstances of Scotland's relationship in the UK could prompt a second referendum. Former leader and MP Alex Salmond has said another vote is "inevitable", and the only question is the timing.