Members of the public have been advised to stay at home as much as possible, with sports fans told to take lateral flow tests if they decide to go to games.
Rangers are due to play Dundee United at Ibrox on Saturday, while Hampden will host a cup final match between Celtic and Hibernian on Sunday.
Ms Sturgeon said: “Please limit your social interactions – whatever your social interactions would normally be, limit them as much as you can right now.
“I’m asking people – and I’m not doing this lightly after two years of this – I’m asking people to stay at home as much as they can.”
She continued: “Had we the kinds of 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.”
She asked people to “think carefully about every interaction you’re having”.
Mr Smith said Omicron is more transmissible than previous variants of Covid-19.
Speaking about football fans, he said: “Whether they’re vaccinated or not, I would encourage them very, very strongly to make sure they’re taking lateral flow tests before they go.
“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 and cars you’re going to be in going to the game.”
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