The First Minister said if the Scottish Parliament has to give its consent, she would “of course” consider asking MSPs not to do this.
In Scotland 62% of people voted to stay in the European Union (EU), a situation in stark contrast with the result of the UK-wide vote, which saw 52% opt to leave.
With the UK now “in turmoil”, the SNP leader said she would “find it hard to believe” that Holyrood would not be required to back the UK leaving the EU.
Scottish Secretary David Mundell said he did not think the Scottish Parliament would be “in a position to block Brexit”.
Ms Sturgeon, however, stressed that the UK was in “uncharted territory” in the wake of the referendum result and “all of the complexities that have been thrown up by the vote on Thursday”.
With laws passed by Holyrood required to comply with European legislation on human rights, she was pressed on the issue on BBC’s Sunday Politics Scotland.
Ms Sturgeon said: “The issue you’re talking about is whether there would require to be a legislative consent motion, or motions in the Scottish Parliament for the legislation that extricates the UK from the European Union.
“Looking at it from a logical perspective I find it hard to believe that there wouldn’t be that requirement, I suspect the UK Government will take a very different view on that and we’ll have to see where that discussion ends up.”
When asked if she would consider asking the Scottish Parliament not to back a motion for legislative consent, she stated: “Of course, if the Scottish Parliament was judging this on the basis of what’s right for Scotland then the option of saying we’re not going to vote for something that is against Scotland’s interests, of course that is on the table.”
She continued: “I care about the rest of the UK, I care about England, that’s why I’m so upset at the UK wide decision that’s been taken. But my job as First Minister, the Scottish Parliament’s job, is to judge these things on the basis of what’s in the interests of people in Scotland.”
She said she could imagine the “fury” such a move could spark in England, but added: “It is perhaps similar to the fury of many people in Scotland right now as we face the prospect of being taken out of the European Union against our will.”
But Mr Mundell insisted: “We have to respect the result on Thursday, even if we don’t like it. It was a vote by people across the UK as to whether or not the UK remained in the EU.”
The UK Government minister, who had campaigned for the UK to remain in Europe, added: “I personally don’t believe the Scottish Parliament is in a position to block Brexit.”