It comes amid increasing concern over the Omicron variant of Covid-19, which has now overtaken Delta in Scotland and risks “overwhelming” the NHS.
Asked if it was wise to allow so many people to gather during the emergency, Ms Sturgeon told a Covid-19 media briefing on Friday she would be able to give clearer advice if the UK Government had agreed to requests to release funding for compensation.
Chief medical officer Gregor Smith urged spectators to take a lateral flow test before travelling to the match, and to stay away if they have symptoms.
Ms Sturgeon said: “I'm asking people in the run up to Christmas to stay at home as much as they can, and much more than people would normally be doing at this time of year.
“Had we the financial support mechanisms in place that were in place earlier in the pandemic, I would be more able perhaps to give straightforward advice to events to say don’t have these events go ahead right now.
“I can't do that when I can’t compensate people … we need to get these financial mechanisms in place so that across the UK, we can take the steps that we think are necessary.”
Dr Smith asked fans to think about the impact of their attendance on others, and limit possible spread of the virus.
“People who decide to go to the football … over the course of the weekend, whether they are vaccinated or not, I would encourage them very, very strongly to make sure that they are taking lateral flow tests before they go,” he said.
“And please, if you’re symptomatic at all, don’t go to the football.
“Don't risk spreading it to others. Don't risk spreading it amongst the coaches, or the cars that you're going to be in going to the game.
“Because if there's someone with that infection on board the coach, it’s very likely that others on board will contract it as well.
“So just think about the impact that you can have on others, and how you can safeguard that.”