She said the Scottish government would begin preparing legislation to enable another independence vote.
Scotland voted in favour of the UK staying in the EU by 62% to 38%.
The UK as a whole has voted to leave, by a margin of 52% to 48%, prompting UK Prime Minister David Cameron to announce he would stand down by October.
The SNP manifesto for May`s Holyrood elections said the Scottish Parliament should have the right to hold another referendum if there was a "significant and material change" in the circumstances that prevailed at the time of the 2014 referendum, such as Scotland being taken out of the EU against its will.
At a news conference in Edinburgh, Ms Sturgeon said: "It is, therefore, a statement of the obvious that a second referendum must be on the table, and it is on the table," she said.
The Scottish government`s resilience committee, which meets in times of emergency, is due to meet on Friday afternoon. Ms Sturgeon said the Scottish cabinet would meet on Saturday and she would make a statement to MSPs on Tuesday.
The first minister said there was now a significant divergence between Scotland and the rest of Britain which she "deeply regretted".
A majority of voters in all 32 council areas in Scotland voted Remain.
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