The First Minister said the UK Government's EU departure plans would "undermine workers rights rights, environmental standards and social protections."
Prime Minister Theresa May will set out more detail on her plans for Brexit tomorrow, but has already indicated she is ready to leave the EU single market, with Chancellor Philip Hammond having warned of a "radical change" to the UK economic model.
Ms Sturgeon said such a scenario would be "deeply troubling" after Brexit.
"That should deeply trouble everybody because it becomes then not just a question of should we be in or out of the EU," she told Sky News.
"That actually starts to become a fundamental question of what kind of country to we want to be."
Mr Hammond warned in a weekend interview that the UK will do "whatever we have to do" to remain competitive if the country is forced to leave the single market, prompting speculation that this could lead to big cuts in corporation tax.
Ms Sturgeon warned this will result in a "low tax, low wage, deregulated economy."
"Whether they voted leave or remain that starts to raise pretty profound and fundamental questions about what kind of country we want to be - and for Scotland not just what kind of country we want to be, but who gets to decide that, because this is not a path that the majority of people in Scotland decided to take."
The EU referendum in June saw 62% of Scots vote to remain, while 38% opted to leave. The weight of votes south of the border swung the outcome in favour of Brexit.
Ms Sturgeon added: "I've been very clear that the option of an independence referendum has to be on the table because if it isn't then Scotland risks being taken down a really damaging path with no control over the future of our own country."