Scotland had rejected independence in a 2014 referendum but Sturgeon said the landscape had changed since then due to Thursday's seismic national vote to leave the European Union.
The United Kingdom -- as it was when Scotland voted to stay in it -- "does not exist any more", she said.
Britain as a whole voted by 52 percent to 48 percent to leave the EU but Scotland voted strongly for Britain to remain -- by 62 percent to 38 percent.
"What's going to happen with the UK is that there are going to be deeply damaging and painful consequences... I want to try and protect Scotland from that," Sturgeon told the BBC's Andrew Marr Show.
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Scots rejected independence two years ago by a margin of 55 percent to 45 percent, but surveys taken after Thursday's vote showed most would now back going it alone.
A Panelbase survey for the Sunday Times found 52 percent of respondents wanted to break with the rest of Britain, while 48 percent were opposed.
In a round of broadcast interviews, Sturgeon also said it was possible that the Scottish parliament may have to give its consent to laws to extricate Britain from the EU.
Asked whether she would consider asking Scottish lawmakers not to give that consent, she replied: "Of course."
However, Adam Tomkins, an opposition Scottish lawmaker and professor of public law at Glasgow University, said the government did not have the right to bloc a Brexit.
"Holyrood has the power to show or to withhold its consent," he wrote on Twitter, referring to the seat of government in Edinburgh.
Sturgeon leads the pro-independence Scottish National Party, which has 63 out of 129 seats in the devolved parliament, as well as 54 out of 650 seats in Britain's House of Commons lower house of parliament.
Setting out Scotland's negotiating position with Brussels, Sturgeon said that the country would not need to rejoin the EU as a new member state because it would never leave.
"Our argument is that we don't want to leave. It's not that we want to leave and get back in," she said.
She also cautioned any future British prime minister against vetoing a new Scottish independence vote.