The First Minister urged demonstrators not to resort to violence, but expressed confidence that the event would be policed appropriately.
She said: “Come out, make your voice heard, do so peacefully.
"I am a very strong supporter of peaceful democratic protest.
"It is a powerful agent for change, and in the climate context, the United Nations actively encourages peaceful protest as part of the COP process, so [I’m] a big supporter of that.
"Clearly, I don’t condone violent demonstrations and the police will respond as they consider appropriate to that.”
Between 50,000 and 100,000 people are expected to take part in the march through the city centre to a rally on Glasgow Green.
Ms Sturgeon said she had faith in Police Scotland’s approach following claims of heavy handedness in dealing with some COP26 protests this week.
She said: "How demonstrations are policed is an operational matter for the chief constable, and I, as a politician, should not be seeking to dictate how that is done.
“I know the chief constable is very, very keen and supportive of the role the police have to facilitate peaceful protest.
"The approach that will be taken to that I have confidence will be the right and the appropriate one.”
Ms Sturgeon said she would not be joining the march, partly because of other commitments such as co-chairing the Under2 coalition campaigning to keep global temperature rise below 2C.
She said: “I might not be on the march physically but I will certainly be with the loud, peaceful protesters in spirit.
"I’m not saying I’ll never go on a demonstration...but I’m somebody the protesters rightly are trying to push to go further, and that’s the dynamic there.”
Ms Sturgeon acknowledged some protesters felt less optimistic about the COP26 talks than those directly involved, but said events like the march could accelerate progress.
Speaking within the COP26 conference venue, she said: "I don’t want to overstate this or in any way count the chickens around this, [but] there is a greater degree of optimism inside this place about the progress that might be made between now and the end of next week.
"I hope that is justified at the end of the day, but looking at some of the detail, I think that slight increase in optimism is justified.
"But I do think there’s still a gap between the optimism in here and the sense outside that they’re not feeling that.
"There’s a gap there that has to be bridged, but protest is part of bridging that – it’s about making the voices of people, not just across the country but across the world, heard in here, so that pushes that process even further.”
However, Ms Sturgeon disagreed that campaigning for Scottish independence should be suspended to focus on tackling climate change, which she described as a “daft argument”.