The rally left Saltmarket around 12.30pm and made its way to BBC Scotland headquarters at Pacific Quay.
A statement on the Facebook page for All Under One Banner, which co-ordinates pro-independence marches across the country, said: "Due to the outrageous decision by the UK Supreme court and the strength of public feeling about this, we will now be marching to the BBC on Saturday. Every day that we live under Westminster rule is another day enduring Westminster harm.”
She told guests that Wednesday’s Supreme Court ruling would “galvanise” the independence movement.
Court president Lord Reed ruled the laws that created the devolved Scottish Parliament in 1999 meant it did not have power over areas of the constitution, including the union between Scotland and England.
Following the judgement, a number of rallies were held around the country.
Ms Sturgeon said: "Wednesday's judgment from the Supreme Court has galvanised the Yes movement right across Scotland. Thousands of people took to the streets - in freezing Scottish winter weather - to demonstrate their support for Scottish democracy."
She added: "The inconvenient truth for Westminster is that, much as they would prefer otherwise, the Scottish independence movement is not going away. Indeed, it is growing. It is strengthening. And it is winning. Because it is now as much a democracy movement as an independence movement."
The First Minister plans to use the next general election as a de facto referendum but the idea has been rejected by both Conservatives and Scottish Labour, who argue that general elections are fought on a range of issues.
Scottish Conservative constitution spokesman Donald Cameron said people "will be dismayed that Nicola Sturgeon is doubling down on the nationalists' obsession, rather than getting back to the day job and tackling the urgent concerns of most Scots".
Meanwhile, Keith Brown, who has served as the SNP's depute since 2018, claimed the movement would "hit new heights” following the Supreme Court ruling.