Ms Sturgeon said it was “democratically unacceptable” that Scotland faced being taken out of the EU against its will.
And she said a second independence referendum was “highly likely”.
Scotland voted in favour of the UK staying in the EU by 62% to 38%, but the UK as a whole voted to leave by a margin of 52% to 48%.
The result saw Prime Minister David Cameron announce he would stand down by October.
Hundreds of people protested against the EU result in Glasgow and Edinburgh on Friday evening.
Ms Sturgeon said there was now a “significant divergence” between Scotland and the rest of Britain which she “deeply regretted”.
She said the meeting of the Scottish cabinet on Saturday morning would “discuss our next steps in more detail”.
‘Best interests’
And she said the Scottish government was to begin preparing legislation to enable another independence vote.
Ms Sturgeon has said she has “clear common cause” with London Mayor Sadiq Khan, who wants London to remain in the EU despite the Brexit vote.
But she has stressed that her priority was to “act at all times in the best interests of Scotland and in a way that unites, not divides us”.
Is the time right for Indyref2? – BBC Scotland political editor Brian Taylor
It looks “highly likely”, says Nicola Sturgeon, that there will now be a second referendum upon Scottish independence.
Is she enthused by this prospect? Does she thrill at the notion? Is she buffing up her best lines from 2014? The answers to those questions would be no, no and, once again, no.
To be clear, for the avoidance of any doubt, Nicola Sturgeon remains rather keen on the concept of Scottish independence. Indeed, she yearns for it.
She knows that means another referendum at some point in the future. But not now. Not in these circumstances. Not in these troubled times.
Opposition leaders at Holyrood – who all backed Remain ahead of the referendum – shared Ms Sturgeon’s disappointment at the result.
But both Ruth Davidson of the Conservatives and Scottish Labour’s Kezia Dugdale said it did not justify holding another independence referendum.
Ms Davidson said an independence vote would not help the country achieve stability, and was not in the best interests of the people of Scotland.
She added: “The 1.6 million votes cast in this referendum in favour of remain do not wipe away the two million votes that we cast less than two years ago.
“And we do not address the challenges of leaving the European Union by leaving our own Union of nations, our biggest market and our closest friends.
“I believe in Scotland’s place within the United Kingdom today as much as ever.”
How has Scotland reacted to the Brexit vote?
BBC Scotland took to the streets of towns and cities across the country to find out what people feel about the decision to leave the EU.
Ms Dugdale said she and Ms Sturgeon had “profound disagreements”, about the constitutional future of Scotland, but said she stood ready to work with the first minister in the best interests of the people of Scotland.
She added: “Now is the time for calm heads. Labour’s manifesto ruled out a second referendum in the lifetime of this parliament – we won’t be changing our minds any time soon.
“On the question of independence, many of the fundamental questions that were unresolved and unanswered in 2014, remain so. Not least the question of currency. What we don’t need today is more turmoil, more upheaval and more economic chaos.”
The Scottish Greens, who support independence, have launched an online petition calling on Holyrood to “examine and exhaust every option for continuing Scotland’s close ties with Europe”. Reports by BBC,
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